Boat B's relative bearing to Boat A is 27.65
Relative bearing: What is it?The angle between the travel direction and another direction is known as the relative bearing. From the current direction, this angle is measured in a clockwise motion. As an illustration, a ship is now moving at a bearing of 050°. From the ship's present direction, a relative bearing of 010° is calculated. Bearings can be used to show both the direction and the angle of a certain location. In math, bearings are three-digit angles measured clockwise from a protractor's zero-degree point. On your GCSE math test, the north direction (or starting point) is typically given in the question text.
Given the data, we can infer that
According to the Pythagoras Theorem,
In a right triangle,
c²=a²+b²
where
c is the hypotenuse
a and b are the legs
In this problem
Let
c ----> the distance between the boats
a -----> the horizontal distance between the boats
b -----> the vertical distance between the boats
substitute the values,
c²=21²+18²
c=√(21²+18²)
c=27.65
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A line with a slope of – 1/6 passes through the points (1,3) and (7,f). What is the value of f?
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: f = 2[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Let's consider two points (1 , 3) and (7 , f), now we can write the slope (m) of line in form of these points as :
[tex] \qquad \tt \rightarrow \: m = \cfrac{y2 - y1}{x2 - x1} [/tex]
[tex]\qquad \tt \rightarrow \: - \dfrac{1}{6} = \dfrac{f - 3}{7 - 1} [/tex]
[tex]\qquad \tt \rightarrow \: - (7 - 1) = 6(f - 3)[/tex]
[tex]\qquad \tt \rightarrow \: - 6 = 6(f - 3)[/tex]
[tex]\qquad \tt \rightarrow \: f - 3 = - \dfrac{6}{6} [/tex]
[tex]\qquad \tt \rightarrow \: f - 3 = - 1[/tex]
[tex]\qquad \tt \rightarrow \: f = - 1 + 3[/tex]
[tex]\qquad \tt \rightarrow \: f = 2[/tex]
Value of f is 2, so the point is : (7 , 2)
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Select the TWO numbers that are solutions to the equation x³ = 27.
□A√27
□ C √27
□D 27³
DE 9
Cube roots - The two numbers that are solutions to the equation x³ = 27 are +3 and -3.
What are cube roots?
A number's cube root is a quantity that, when multiplied by itself three or more times, returns the original quantity. The cube root of 27, represented as 327, for instance, is 3 because 3 x 3 x 3 = 27 = 33 when we multiply 3 by itself three times. As a result, we can state that the cube root yields a value that is essentially cubed. Here, 27 is referred to as the ideal cube. We may deduce what the cube's root is from the word "cube root." It denotes the integer that brought about the cube under the root. Typically, we use the prime factorization technique to determine the cubic root of perfect cubes. We can discover the importance of square root in a similar way.
We are given the equation,
[tex]x^{3}[/tex] = 27
taking cube root on both the sides to find the value of x,
we get,
x = ±[tex]\sqrt[3]{27}[/tex]
further solving,
x = ±3.
Hence the two solutions of the x³ = 27 equation will be ±3 or +3 and -3.
Because 3x3x3 Equals 27, the cube root of 27 is 3.
Since 4x4x4 = 64, the cube root of 64 is also 4, and so on.
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Which ordered pairs in the form (x, y) are solutions to the equation 4x - 5y = 24 Select each correct answer.
(6,0)
(4,8)
(1,-4)
(-9, -12)
The ordered pairs (x, y) which are the solutions to the equation 4x - 5y = 24 are option A (6, 0), option C (1, -4) and option D (-9, -12)
Given,
The equation: 4x - 5y = 24
We have to find the ordered pairs in the form (x, y) which are the solutions to the equation:
Lets check:
Option A: (6, 0)
Substitute this in the equation:
We get
4 × 6 - 5 × 0 = 24
24 - 0 = 24
24 = 24
(6, 0) satisfies the equation.
Option B: (4, 8)
Substitute this in the equation:
We get
4 × 4 - 5 × 8 = 24
16 - 40 = 24
-24 ≠ 24
(4, 8) does not satisfies the equation.
Option C: (1, -4)
Substitute this in the equation:
We get
4 × 1 - 5 × -4 = 24
4 - (-20) = 24
4 + 20 = 24
24 = 24
(1, -4) satisfies the equation
Option D: (-9, -12)
Substitute this in the equation:
We get
4 × -9 - 5 × -12 = 24
-36 + 60 = 24
24 = 24
(-9, -12) satisfies the equation
Therefore, the solutions for the equation 4x - 5y = 24 are option A (6, 0), option C (1, -4) and option D (-9, -12)
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a grain of salt has an approximate length of 9.8x10 to the -4 feet. The approximate height of Mt. Everest is 2.9035x10 to the power of 4 feet. Calculate the approximate number of grains of salt it would take to reach the height of Mt. Everest..
The approximate number of grains of salt it would take to reach the height of Mt. Everest is; 0.2963 * 10⁸
How to divide exponents?We are given;
Approximate length of a grain of salt = 9.8 * 10⁻⁴ ft
Approximate height of Mt. Everest = 2.9035 * 10⁴ ft
Now, we want to know the approximate number of grains of salt it would take to reach the height of Mt. Everest. To get this it means we have to divide the Approximate height of Mt. Everest by the Approximate length of a grain of salt.
According to Laws of exponents, we know that;
x³/x² = x^(3 - 2) = x¹
Thus;
Approximate number of grains of salt it would take to reach the height of Mt. Everest = (2.9035 * 10⁴)/(9.8 * 10⁻⁴) = (2.9035/9.8) * (10⁴⁻⁽⁻⁴⁾) = 0.2963 * 10⁸
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Since three bits can be used to represent numbers between 0 and 7, we could use three bits to store the size of most families. Three bits wouldn’t be sufficient to store the number of students in a typical discussion section as they run anywhere from 15 to 25 students and three bits can only store numbers from 0 to 7.
How many binary digits would we need to set aside in order to store the number of high school students taking CS105 across the nation (we have 220 high school students in total)?
Considering the numerical representation of integers with n bits, it is found that 8 bits would have to be set aside in order to store the number of high school students taking CS105 across the nation.
What is the range of the binary representation of unsigned numbers with n bits?For this problem, we work with unsigned numbers, excluding negatives, as the number of students is a discrete amount that starts with 0 and increases by 1 for each new student.
For unsigned integers with n bits, we have that:
The minimum value that can be represented is: 0.The maximum value that can be represented is: 2^n - 1.For this problem, we want to represent an amount of 220, hence the number of bits needed is found as follows:
2^n - 1 ≥ 220
2^n ≥ 221
log2(2^n) ≥ log(2)(221)
n ≥ 7.8.
The number of bits cannot be a decimal amount, hence n is rounded up, and thus, 8 bits are needed to represent the amount.
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The growth rate of the virus that causes covid-19 is 24% compounded continuously. If
a sample of the virus has 125 cells, how many cells will be present in the sample after
5 days? Round your answer to the nearest cell.
166.25E + 4500 cells will be present in the sample after 5 days.
How to find the number of cells present?Given,
Cells 24% compounded continuously,
A sample of the virus has 125 cells.
To find:
No cells will be present in the sample after 5 days
Solution:
a = p ( 1 + r/n)nt
a = 125 ( 1 + 24/24)^24*5
a = 125(2)^120
a = 125 * 1.3292279957849E+36
a = 166.25E + 4500
166.25E + 4500 cells will be present in the sample after 5 days.
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find the value of x and the measure of each angle
Answer:
see explanation
Step-by-step explanation:
since QR ≅ RS , the triangle is isosceles with base angles congruent, so
∠ Q = ∠ S , that is
8x - 17 = 5x + 1 ( subtract 5x from both sides )
3x - 17 = 1 ( add 17 to both sides )
3x = 18 ( divide both sides by 3 )
x = 6
Then
∠ Q = 8x - 17 = 8(6) - 17 = 48 - 17 = 31°
∠ R = 19x + 4 = 19(6) + 4 = 114 + 4 = 118°
∠ S = 5x + 1 = 5(6) + 1 = 30 + 1 = 31°
Evaluate the equation
f(n) = -2n + 1
ƒ (12) =
Hello!
To find f(12):
⇒ must plug in '12' into the x's position in the equation
[tex]f(12)=-2(12) +1=-24+1=-23[/tex]
Hope that helps!
given=1/5x-5=5 prove x=50
Prove that x = 50 in the following equation: 1/5x – 5 = 5
Write the equation:
1/5x – 5 = 5
Add 5 to both sides:
1/5x – 5 + 5 = 5 + 5
1/5x = 10
Multiply each side by 5:
5 × 1/5x = 10 × 5
–5 + 5 cancels out, leaving you with:
1x = 10 × 5
1x = 50
Divide both sides by 1 to get x:
1x/1 = 50/1
The 1 cancels out:
x = 50/1
Answer:
x = 50 ✔
Check your work by plugging in 50 as x:
1/5x – 5 = 5
1/5 × 50 – 5 = 5
Multiply:
1/5 × 50/1 – 5 = 5
50/5 – 5 = 5
Get rid of the fraction by dividing:
50 ÷ 5 = 10
10 – 5 = 5
Subtract:
10 – 5 = 5
5 = 5 ✔
I have just proven that x = 50 because the answer I got when I checked my work was balanced. Hope that helps! Have an amazing rest of your day! :)
A salesman sellls a car for $10,500. If he paid a commission of 5% for the first $10,000 and 8% on the remainder, what’s the total commission
Using percentages we can conclude that the total commission the salesman gets is of $540.
What is the percentage?A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a part per hundred. Per 100 is what the word percent means. By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.So, the total commission:
5% of 10,000 -
10,000/100 × 5 = $5008% of remaining (10,500 - 10,000 = 500) $500 -
500/100 × 8 = $40Total commission: $500 + $40 = $540
Therefore, using percentages we can conclude that the total commission the salesman gets is of $540.
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WILL MARK BRAINLEIST!
(02.02 MC)
Use the graph to fill in the blank with the correct number.
f(0)=______
1
0
-2
-3
Answer:
The answer is 1
Determine the values of y in the equation y2 = 144.
a. y = ±12
b. y = ±72
c. y = 12
d. y = 72
The value of y is +12 or -12 or y = ±12 if the quadratic equation is y² = 144 option (A) y = ±12 is correct.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
It is given that:
The quadratic equation is:
y² = 144
As we know, the polynomial equation is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
Taking square root on both sides:
y = ±√144
y = ±12
Thus, the value of y is +12 or -12 or y = ±12 if the quadratic equation is y² = 144 option (A) y = ±12 is correct.
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What is the value of x?
A. x = 32
B. x = 37
C.x = 58
D. x = 148
LET US FIRST FIND m<FEG using sum of angles in a triangle
[tex]58 + 90 + < feg = 180 \\ < feg = 180 - 90 - 58 \\ < feg = 32[/tex]
NOW WE CAN SEE THAT <FEG +<E =180° BECAUSE THEY ARE ON A STRAIGHT LINE.
[tex] < feg + 4x = 180 \\ 32 + 4x = 180 \\ 4x = 180 - 32 \\ 4x = 148 \\ \frac{4x}{4} = \frac{148}{4} \\ x = 37[/tex]
THEREFORE x=37°
R is inversely proportional to A.
R = 12 when A = 1.5
a) Work out the value of R when A = 5.
b) Work out the value of A when R = 9
Inversely proportion - The work out value of R and A is 3.6 and 2 respectively.
What is inversely proportion?
They are said to be inversely proportional when one quantity's value rises relative to another's decline or vice versa. It implies that the two quantities behave inherently differently. For instance, time and speed have an inverse relationship. The time decreases as you increase the speed. Inverse proportion, varying inversely, inverse variation, and reciprocal proportion are additional terms used here to describe this kind of proportion.
Given, R [tex]\alpha[/tex] 1/A
R = k/A
When R = 12 and A = 1.5
12= k× 1.5
k= 18
Now, when A=5, R= 18/5 = 3.6
And when R= 9, A = 18/9=2
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Question 2(Multiple Choice Worth 4 points)
(01.02 MC)
A foreign exchange student from Denmark would like to buy gifts for her family. She finds a special deal, 7 t-shirts for $97.93, that
she would like to purchase for her family. However, her family only consists of 5 people. If she wants to purchase 5 t-shirts for her
family members at that special rate, what would be the cost of these t-shirts in her currency of Krona? (Currency conversion rate is 1
U.S. Dollar = 8.6964 Krona)
O 121.663 Krona
O 13.99 Krona
608.313 Krona
2
69.95 Krona
The cost of the 5 t-shirts in her currency of Krona is 608.313 Krona.
How do you make a currency conversion?The formula for converting currencies is Original Currency / New Currency = Exchange Rate.
Given:
Cost of 7 t-shirts at a special deal = $97.93
Now, she wants to purchase 5 t-shirts for her family members at this special rate.
Total Cost of 5 shirts in dollars = (97.93 * 5)/7 = $69.95
The exchange rate of the currency is 1 U.S. Dollar = 8.6964 Krona
So, $69.95 = (69.95 * 8.6964)/1 = 608.313 Krona
Therefore, the cost of the 5 t-shirts in her currency of Krona is 608.313 Krona.
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classify the equation 10x+22x-5=8(4x+7)?as having one solution,no solution,or infinite many solutions
On the east side of Holly Hill, you climb 2 feet higher for every 11 yards you climb toward the west. If you climb the hill to a height of 12 feet, how far west have you moved from the foot of the hill?
Based on the height climbed, and the yards climbed per feet, the distance west you would have moved from the foot of the hill is 66 yards
How to find the distance moved?For every 2 feet that you climb higher, you would be moving about 11 yards to the west.
This means that the distance climbed is directly proportional to the number of yards to the west.
Every 2 feet that one climbs higher will meant they move 11 yards to the west so the yards to the west for 12 feet is:
= 12 / 2 x 11
= 6 x 11
= 66 yards
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Help me with this question pleaseeeeeee
Answer:
False
Step-by-step explanation:
Scale copies are indicated by proportional changes in the lengths of the sides of a figure. in this image, we can see that the bottom side of the figure is different while the shorter segments on each figure are the same length. Because of this, the answer is False as they can not be scale copies.
What value of x makes this equation true?
X/2-2= X/4+4
A. 4
B. 8
C. 16
D. 24
Please help me :'(
The value of x that makes this equation (X-2)/2= (X+4)/4 to be true is 8.
What is an equation?An equation ca be described as the mathematical terms which can contains different digits as well we a as alphabet and it can simplified so that a particular expression or term can be found, in the given equation we were told to find the value of x by simplify the equation which is done below.
(X-2)/2= (X+4)/4
Then if we cross multiply we will have
(4x - 8) =(2x+8)
then we can simplify further and collect the like terms which is
2x=16
x=8
There, the correct option is B
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3.3615 rounded to the nearest tenth
The answer is 3.4
Because the 3 is in the tenths place. Since 6 is greater than 5 it gives 1 to the 3 which makes it a 4.
Ava's bedroom has an area of 36 square feet. The bedroom is 6 times as many square feet as Ava's closet. If the closet is 3 feet wide, what is the length of the closet?
First find the area of the closet.
Answer:
The area of Ava's closet is 2 square feet.
Step-by-step explanation:
The area of the bedroom is 36 and it is 6 times as many square feet as her closet. They are basically saying that the closet has 1/6th the area of the bedroom.
Now we can form an equation to find the area of her closet.
36 ÷ 6 = 6
So, therefore, the area of the closet is 6 square feet.
We know the width of the closet, which is 3 feet. Since the formula of area for her closet is Length × Width, we can form an equation for this.
X in this equation is what we are trying to solve for, which is the length of the closet.
X = 6 ÷ 3
X = 2
So, therefore, the area of Ava's closet would in the end be 2 square feet.
Let me know if you have any questions! :)
How
many solutions does this nonlinear system of equations have?
The nonlinear system of the equation has two solutions as it intersects at two points.
What is the graphical solution of a system of equations?Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
From the given figure we observe that the straight line intersects the parabolic curve at two distinct points, Therefore this nonlinear system of equation has two solutions.
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i need help on this, thanks
Answer:
x=15, y=7
Step-by-step explanation:
Angles that form a linear pair are supplementary, so:
[tex]2(5x-5)+3x-5=180 \\ \\ 10x-10+3x-5=180 \\ \\ 13x-15=180 \\ \\ 13x=195 \\ \\ x=15 \\ \\ \\ \\ 5y+5+20y=180 \\ \\ 25y+5=180 \\ \\ 25y=175 \\ \\ y=7[/tex]
What is the slope of the line?
the slope of the line on the graph is 3 .
What is slope of a line ?Slope is calculated by dividing the "vertical change" by the "horizontal change" between any two distinct points on a line. The ratio can alternatively be expressed as a quotient, which yields the same result for any two separate locations on the same line ("rise over run"). A negative "rise" indicates a falling line. A road surveyor may judge that the line is useful, or it may show up in a diagram of a road or a roof as a description or a design. The steepness, incline, or grade of a line can be measured using the slope's absolute value. A slope with a larger absolute value denotes a steeper line.
Calculationto find the slope of the graph we will take two points which lies on the same line i.e. they must be collinear .
the points i m choosing is (-2,0) and (-1,3)
now for finding the slope we will use the formula
m = (y2-y1)/(x2-x1)
m = (3 - 0 ) / (-1+2)
m = 3 / 1
m = 3
so the slope of the line on the graph is 3 .
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Find the value of r so that the line that passes through each pair of points has the given slope:
(r, -2) (10, 1) and the slope of the line is 1/4
4. 8(c - 9) = 6(2c - 12) - 4c
c = All real numbers are solutions.
How is the equation 8(c - 9) = 6(2c - 12) - 4c solved?
8(c - 9) = 6(2c - 12) - 4c
8c- 72 = 12c- 72- 4c
8c- 72 = 8c - 72
0=0
L.H.S = R.H.S
Both sides are equal and this stands true for all real number values as c.
For example:
Let c = 10
8(10) - 72= 8(10) - 72
8 = 8
L.H.S = R.H.S
What are real numbers?
Real numbers are the values of continuous quantities that can be used to indicate distances along lines It is a quantity that can be represented as an infinite decimal expansion.Real numbers can be pictured as points on the number line or real line, which is an indefinitely long line where the points corresponding to integers are evenly spaced. While both the set of all natural numbers and the set of all real numbers are infinite sets, the set of all real numbers is uncountable in the sense that there cannot be a one-to-one function from the real numbers to the natural numbers.To learn more about real numbers, refer:
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Estimate a 15% tip on a dinner bill of 59.17 by first rounding the bill amount to the nearest ten dollars.
well, the bill was $59.17, if we round it by the "tens", the closest to 59 is 60, since 59 is farther from 50 but closer to 60, so it rounds up to 60
[tex]50\stackrel{farther}{\rule[0.35em]{18em}{0.25pt}59.17}\stackrel{closer}{\rule[0.35em]{2em}{0.25pt}}60 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 60}}{\left( \cfrac{15}{100} \right)60}\implies 9[/tex]
log6 8+ 2log6 3+log6 12-log6 24
after simplifying the logarithm expression log₆ 8 + 2log₆ 3 + log₆ 12 - log₆ 24, we get the result as log₆ 36.
We are given the logarithm expression as:
log₆ 8 + 2log₆ 3 + log₆ 12 - log₆ 24
Now, we can also write 2log₆ 3 as:
2log₆ 3 = log₆ 3²
So, the logarithm expression will become:
log₆ 8 + log₆ 3² + log₆ 12 - log₆ 24
Now, we will use the property that is:
logₐ x + logₐ y = logₐ (x × y)
So, we get the logarithm expression as:
log₆ ( 8 × 3² × 12 / 24)
=log₆ (8 × 9 × 12 / 24)
= log₆ (36)
= log₆ 36
Therefore, after simplifying the logarithm expression log₆ 8 + 2log₆ 3 + log₆ 12 - log₆ 24, we get the result as log₆ 36.
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The height of a woman can be predicted by the equation h = 81.2 +3.34r, where his her height in centimeters and ris
the length of her radius bone in centimeters.
a. Write the equation in standard form.
h=
b. Find the r- and h-intercepts. Round to the nearest hundredth.
h-intercept =
r-intercept =
c. Use the function to find the approximate height of a woman to the nearest centimeter whose radius bone is 25 centimeters long.
cm
Using the given linear function, we have that:
a) The equation in standard form is: h - 3.34r - 81.2 = 0.
b) The intercepts are given as follows: h-intercept = 81.2, r-intercept = -24.31.
c) The predicted height is of 164.7 centimeters.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In standard format, the equation is given by:
y - mx - b = 0.
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, the equation is:
h = 81.2 + 3.34r.
In standard format, the equation is:
h - 3.34r - 81.2 = 0.
From the equation, the h-intercept is of 81.2. To find the r-intercept, we have to solve for r when h = 0, hence:
3.34r + 81.2 = 0.
3.34r = -81.2
r = -81.2/3.34
r = -24.31.
For item c, the radius is given by r = 25, hence the height will be given as follows:
h = 81.2 + 3.34(25) = 164.7.
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Use the graph to find the values below.
From the given graph, the numeric values of the expressions are given as follows:
f(-1) = 12.f(1) - g(1) = 8.g(x) = 4 when x = 2.f(x) = g(x) when x = 3.How to find the numeric value of a function or of an expression?To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.
On the graph of the function, the equivalent to this is that we have to find where the x-axis has the value, and find the value of y for which the function passes through the y-axis.
From the graph, when x = -1, f(x) passes the point at y = 12, hence f(-1) = 12.
For the second item, applying the same logic, we have that:
f(1) = 10.g(1) = 2.Hence:
f(1) - g(1) = 10 - 2 = 8.
For the third item, we have to look at the graph of g(x), and find the value of x when y = 4, hence g(x) = 4 when x = 2.
For the fourth item, the functions intersect at point (3,8), hence f(x) = g(x) when x = 3.
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