Answer:
y = 6x + 1
Step-by-step explanation:
linear equations (straight line) are expressed in the following general form:
y = mx + b, where m is the gradient and b is the y-ordinate of the point where the line crosses the y-axis (called the y-intercept)
Given : m = 6
we realize that point (0,1) is actually on the y-axis (i.e x=0), therefore this is coincidentally the y-intercept. Hence b = 1
Therefore the whole equation is
y = 6x + 1
The equation for a line is:
y = mx + c
Note:
y is the y coordinate
m is the slope
x is the x coordinate
c is the y -intercept (where the line crosses the y-axis.
The question tells us that the slope is 6 (so m is 6)
It also tells that the coordinates are: (0 , 1) (so x is 0 and y is 1)
Lets plug in these values into the equation and solve to get the missing value ( which is c) :
y = mx + c
1 = 6(0) + c
1 = c.
Now to get the equation of the line, we plug in the values for m and c into y= mx + c:
Equation of line: y = 6x + 1
-----------------------------------------------------------
Answer:
Equation of line with slop m = 6 and including point (0, 1) is:
y = 6x + 1
Which point lies on a circle with a radius of 5 units and center at P(6, 1)?
A. Q(1, 11)
B. R(2, 4)
C. S(4,-4)
D. T(9,-2)
Answer:
The correct answer is R(2, 4)
Step-by-step explanation:
Write the point-slope form of an equation of the line through the points (-2, -3) and (-7, 4).
Answer:
y+3 = -7/5(x+2)
Step-by-step explanation:
First we need to find the slope
m = (y2-y1)/(x2-x1)
= (4--3)/(-7--2)
= (4+3)/(-7+2)
=7/-5
= -7/5
The point slope form is y-y1 = m(x-x1)
y--3 = -7/5(x--2)
y+3 = -7/5(x+2)
We could use the second set of points
y-4 = -7/5(x--7)
y-4 =-7/5(x+7)
Drag each tile to the correct box.
Ratio Conversion Table
kilometer (km) : meter (m) 1 : 1,000
meter (m) : centimeter (cm) 1 : 100
centimeter (cm) : millimeter (mm) 1 : 10
Using the conversion table, arrange the measures in order from least to greatest.
5,000 cm
5,000 m
50 cm
550 mm
5,000 mm
Answer:
1. 50 cm
2. 550 mm
3. 5000 mm
4. 5000 cm
5. 5000 m
Step-by-step explanation:
We can convert all the measures in same unit to arrange them one by one.
5000 cm:
As there are 10 millimeters in 1 cm,
5000 cm = 5000*10mm
=> 50000 mm
5000 meters:
As there are 100 cms in one meter
5000 m = 5000*100 cm
=> 500000 cm
Now to convert in millimeter
500000*10= 5000000 mm
50 cm:
50*10 = 500 mm
Then there is 550 mm and 5000 mm
So, the order from least to greatest is:
1. 500 mm which is equivalent of 50 cm
2. 550 mm
3. 5000 mm
4. 50000 mm which was equivalent of 5000 cm
5. 5000000 mm which was equivalent of 5000 m ..
Final answer:
To compare the given measurements, we converted each one to millimeters (mm) using a conversion table, then arranged them in ascending order: 50 cm (500 mm), 550 mm, 5,000 mm, 5,000 cm (50,000 mm), and 5,000 m (50,000,000 mm).
Explanation:
To determine which of the given measures is the smallest and which is the largest, we need to convert each measure to the same unit for comparison. Using the ratio conversion table, we will convert all measures to millimeters (mm).
5,000 cm = 5,000 × 10 mm = 50,000 mm5,000 m = 5,000 × 1,000 cm = 5,000,000 cm × 10 mm = 50,000,000 mm50 cm = 50 × 10 mm = 500 mm550 mm is already in millimeters5,000 mm is already in millimetersNow we arrange the measures in order from least to greatest:
50 cm = 500 mm550 mm5,000 mm5,000 cm = 50,000 mm5,000 m = 50,000,000 mmFind the perimeter of the region that is NOT shaded.
39 ft
29 ft
58 ft
See the attached picture:
Find the nth term of this quadratic sequence:
4, 7, 12, 19, 28
Answer:
n² + 3
Step-by-step explanation:
It's a quadratic sequence, so it follows the form:
y = ax² + bx + c
We're given five points that satisfy the equation. (1, 4), (2, 7), (3, 12), (4, 19), and (5, 28). Picking any three points, we can form a system of equations.
If we pick (1, 4), (2, 7), and (4, 19):
4 = a(1)² + b(1) + c
7 = a(2)² + b(2) + c
19 = a(4)² + b(4) + c
4 = a + b + c
7 = 4a + 2b + c
19 = 16a + 4b + c
Through substitution, elimination, or trial and error, we can find a = 1, b = 0, and c = 3.
y = x² + 3
So the nth term of the sequence is n² + 3.
Answer:
a(n) = a(n-1) + (2n - 1)
Step-by-step explanation:
Start by analyzing the pattern:
7 is 3 more than 4;
12 is 5 more than 7;
19 is 7 more than 12, and so on.
Each step is an odd number and is 2 greater than the previous step.
a(2) = 7 = 4 + step = 4 + 3 = 7
a(3) = 12 = 7 + step = 7 + 5 = 12
a(4) = 12 + 7 = 19
a(5) = 19 + 9 = 28
and so on.
Looking at a(2), we see that the step is 2+1, or 3;
Looking at a(3), we see that the step is 2(3) - 1, or 5;
Looking at a(4), we see that the step is 2(4) - 1, or 7; and so on.
Looking at a(n), we see that the step is 2n - 1.
Thus, a(n) = a(n-1) + (2n - 1)
Which of these are arithmetic sequences?
Answer:
D
Step-by-step explanation:
The first and last sequence have a common difference in them. The first having d = 4 and the second having d = 7.
The second and third have a common ratio instead and are geometric sequences. The second has r = 2, and the third having r = (-3)
I ONLY NEED THE 2nd ONE !!
Answer:
The length of the missing side of the triangle is represented by the equation:
(6a + 2b - 5) - (2a - 3b) - (a - 3)
= 6a + 2b - 5 - 2a + 3b - a + 3
= 3a + 5b - 2
Nina graphs the function y = ⌊x⌋ to learn the properties of the parent floor function. What is the value of y when x =5.7?
Answer:
5
Step-by-step explanation:
When you given input of "x" into a floor function y = ⌊x⌋ , it gives as output the "greatest integer less than or equal to x"
For example, if we were to given 1.4 as the input for floor function, it will return the greatest integer that is less than or equal to 1.4, so it would be 1.
So, if we put 5.7 into this function, the floor function would give "5" as the output.
Thus value of y would be 5
Answer:
5
Step-by-step explanation:
Find the factored form of
-14a-a^2=0
Answer:
-a (14 +a) =0
Step-by-step explanation:
-14a-a^2=0
Factor out -a
-a (14 +a) =0
Using the zero product property
-a =0 14+a =0
a =0 a = -14
Write the equation of a line that passed through the point (-2,1) and has a slope of 4
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad ~\hspace{10em}slope = m\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=4[x-(-2)]\implies y-1=4(x+2) \\\\\\ y-1 = 4x+8\implies y=4x+9[/tex]
find the derivative in the form dy/dx
Answer:
dy/dx = [tex]\frac{1}{(4x^{3}-7)}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)}][/tex]
Step-by-step explanation:
* Lets revise some rules for the derivative
- The derivative of ㏑(f(x)) = 1/f(x) × f'(x)
- The derivative of u/v = (vu'-uv')/v²
- The derivative of the constant is 0
* Lets solve the problem
∵ y = ㏑[(4x³ - 7)/(3x^5 + 1)]
- Let u = 4x³ - 7 and v = 3x^5 + 1
∵ u = 4x³ - 7
∴ u' = 4(3)x^(3-1) - 0 = 12x²
∵ v = 3x^5 + 1
∴ v' = 3(5)x^(5-1) + 0 = 15x^4
∵ The derivative of u/v = (vu' - uv')/v²
∴ The derivative of u/v = [tex]\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)^{2}}[/tex]
∵ The derivative of ㏑(f(x)) = 1/f(x) × f'(x)
∴ dy/dx = [tex]\frac{1}{\frac{(4x^{3}-7)}{(3x^{5}+1)}}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4}}{(3x^{5}+1)^{2}}][/tex]
- Simplify by cancel bracket (3x^5 + 1)from the 1st fraction with the
same bracket in the 2nd fraction
∴ dy/dx = [tex]\frac{1}{(4x^{3}-7)}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)}][/tex]
Solve: 5(x + 2) = 3x + 5
A. X=-5/2
B. X=-13/15
C. X=10/11
D. X=5
What is the mean absolute deviation for the set of data below?
2,8,10,16
Answer:
5
Step-by-step explanation:
1. Find the Mean
(2+8+10+16)/4=9
2.For each number, subtract the Mean and square the result.
(2-9)^2=49
(8-9)^2=1
(10-9)^2=1
(16-9)^2=49
3. Find the Mean of those squared differences.
(49+1+1+49)/4=25
4.Take the square root of that and this is what you want.
square root of 25 = 5
If the value of the mean is 9. Then the mean absolute deviation will be 4.
What is the mean absolute deviation (MAD)?It is the average distance between each data point and the mean.
The MAD is given as
[tex]\rm MAD = \dfrac{\Sigma _{i = 1}^n|x_i - \mu|}{n}[/tex]
The data set is given below.
2,8,10,16
Then the mean will be
μ = (2 + 8 + 10 + 16) / 4
μ = 36 / 4
μ = 9
Then the mean absolute deviation will be
MAD = (|2 - 9| + |8 - 9| + |10 - 9| + |16 - 9|) / 4
MAD = (7 + 1 + 1 + 7) / 4
MAD = 16 / 4
MAD = 4
More about the mean absolute deviation link is given below.
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x³ multiplied by x²
plz help and show an explanation not just the answer.
Answer:
[tex]x^{5}[/tex]
Step-by-step explanation:
We simply add the exponents together. This depicts the exponent product rule, which states that when multiplying together two values with the same base (x) but different exponents, we can solve the answer by adding together the exponents with the base staying the same.
Explanation / Proof:
[tex]2^{2} * 2^{3} = 4 * 8 = 32\\\\2^{2} * 2^{3} = 2^{5} = 2*2*2*2*2 = 32[/tex]
As you can see, adding together the exponents will give the same answer. Therefore, the answer is [tex]x^{5}[/tex].
What is 7% of £14.50? Please show me the working outs in a simplest way possible. Thank you
[tex]\text{Hey there!}[/tex]
[tex]\text{The word \bf{of}}\text{ means multiply in mathematical terms.}[/tex]
[tex]\text{Percentages (\%) usually run out of 100}[/tex]
[tex]\text{First, put the numbers set to multiply from each other.}[/tex]
[tex]\text{7\%}\times\text{14.50}[/tex]
[tex]\text{(You can convert the percentage into a decimal (if you want but it is mandatory)}[/tex] [tex]\leftarrow\text{in order for you to convert them into a decimal you have to divide 7\%}[/tex] [tex]\text{from 100}[/tex]
[tex]\dfrac{7\%}{100}[/tex]
[tex]\dfrac{7\%}{100}=0.07[/tex]
[tex]\text{Next, solve for your answer.}[/tex]
[tex]\text{0.07}\times\text{14.50 = ?}[/tex]
[tex]\text{Solve the one above, and you SHOULD get your result!}[/tex]
[tex]\boxed{\boxed{\bf{Thus,\ your\ answer\ is: 1.015}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 785. Find a linear function which fits this data.
Answer:
y = 4.125x + 496.25
Step-by-step explanation:
Set the data up as points. Then deal with the points.
Givens
(30,620)
(70,785)
y2 = 785
y1 = 620
x2 = 70
x1 = 30
Formula
Slope = (y2 - y1) / (x2 - x1)
Solution
Slope = (785 - 620)/(70 - 30)
Slope = 165 / 40
Slope = 4.125
===================
Now you need the y intercept. Either one of the two given points will give you that.
y = 620
x = 30
m = 4.125
y = mx + b
620 = 4.125*30 + b
620 = 123.75 + b
620 - 123.75 + b
b = 496.25
the linear function that describes the relationship between study hours and exam scores is:
y = 4.125x + 496.25
To find a linear function that fits the data provided, we'll use the points (30, 620) and (70, 785), which represent the number of hours spent studying and the corresponding exam scores. The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
First, we calculate the slope (m):
m = (y2 - y1) / (x2 - x1) = (785 - 620) / (70 - 30) = 165 / 40 = 4.125
Next, we use one of the points to solve for b (y-intercept). Let's use the point (30, 620):
620 = 4.125(30) + b
b = 620 - (4.125 × 30) = 620 - 123.75 = 496.25
So the linear function that describes the relationship between study hours and exam scores is:
y = 4.125x + 496.25
Marcel and Floyd are playing games at an arcade. Marcel has $8.25 and is only playing $0.25 games. Floyd has $9.75 and is only playing $0.75 games. Jorge wants to find the number of games after which Marcel and Floyd will have the same amount of money remaining. Jorge’s work is shown below.
Let x = the number of games played.
Jorge knows his answer is incorrect because it does not make sense to have a negative number of games. What is Jorge’s error?
A. The variable x should represent the amount of money left.
B. From Step 1 to Step 2, Jorge did not add 0.25x correctly to both sides.
C. The equation should have sums on both sides.
D. From Step 2 to Step 3, Jorge should have subtracted 0.50x from both sides.
Answer:
The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.
Step-by-step explanation:
If Marcel has $8.25 and is only playing $0.25 games, then the equation will be given by: 8.25 - 0.25X.
If Floyd has $9.75 and is only playing $0.75 games, then the equation will be given by: 9.75 - 0.75X.
If we want to find the number of games after which Marcel and Floyd will have the same amount of money remaining, we need to solve the system of equations:
Equation: 8.25 - 0.25X = 9.75 - 0.75X
Step 1: -1.50 - 0.25X = - 0.75X
Step 2: -1.50 = - 0.50X
Step 3: x=3
The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.
Answer: Option B
From Step 1 to Step 2, Jorge did not add 0.25x correctly to both sides.
Step-by-step explanation:
To solve this problem, let's consider the initial equation that Jorge had.
[tex]8.25-0.25x=9.75-0.75x[/tex]
Subtract 9.75 on both sides of equality
[tex]8.25-9.75-0.25x=9.75-9.75-0.75x[/tex]
[tex]-1.50-0.25x=-0.75x[/tex]
Add 0.25x on both sides of equality
[tex]-1.50-0.25x+0.25x=-0.75x+0.25x[/tex]
[tex]-1.50=-0.50x[/tex]
[tex]x=3[/tex]
You can see then that Jorge's error was adding [tex]-0.75x + 0.25x[/tex]
When this sum is correctly done, the result is [tex]-0.50x[/tex]
The answer is the option B.
what is the slope of the line graphed below? (-1,3) (-2,-1)
Answer:
m=4
Step-by-step explanation:
3-(-1)/-1-(-2)=3+1/-1+2=4/1
Answer:
4
Step-by-step explanation:
Slope formula:
↓
[tex]\frac{\huge Y_2-Y_1}{\huge X_2-X_1}=\frac{Rise}{run}[/tex]
[tex]Y_2=(-1)\\Y_1=3\\X_2=(-2)\\X_1=(-1)\\[/tex]
[tex]\frac{(-1)-3}{(-2)-(-1)}=\frac{-4}{-1}=4[/tex]
Therefore, the slope is 4.
4 is the correct answer.
I hope this helps you, and have a wonderful day!
What is the slope of the line described by the equation y+1=−3x?
Answer:
-3
Step-by-step explanation:
Answer:
The slope of the line is [tex]m=-3[/tex]
Step-by-step explanation:
For a linear equation of the form
[tex]y = mx + b[/tex]
the slope of the line is the constant m
in this case we have the equation
[tex]y + 1 = -3x[/tex]
Solving for y we have:
[tex]y = -3x -1[/tex]
Then [tex]m = -3[/tex]
The slope of the line is -3
A teacher wanted to buy a chair, a bookshelf, two tables and a desk. She spent $900 for all five items and the chair and the desk combined 70% of her total. If the bookshelf cost $50, how much did each of the tables cost?
Find the cost of the chair and desk by multiplying the total amount pent by the 70%
Chair and desk = 900 x 0.70 = $60
Subtract that cost from the total spent:
900 - 630 = $270 was spent on the other three items.
Subtract the cost of the bookshelf:
270 - 50 = 220
The two tables cost 220.
For the price of one table divide that cost by 2:
220/2 = 110
One table cost $110.
The cost of each table is $110.
Given that
There are five items i.e. chair, bookshelf, 2 tables, and a desk.
The total amount incurred for these 5 items should be $900.
And, the chair + desk = 70% of total.
The cost of the bookshelf is $50.
Since 70% of total = chair + desk
That means
Chair + desk = 0.70 of $900 = $630
So the other items cost should be
= $900 - $630
= $270
And, the cost of bookshelf is $50
So, the two tables cost should be
= $270 - $50
= $220
So for one it should be
= $220 ÷ 2
= $110
Therefore we can conclude that the cost of each table is $110.
Learn more about the cost here: brainly.com/question/5282141
I suck at geo and need help!!!
Answer: 45°
Step-by-step explanation:
Because AB and CD are parallel, angle x must be congruent with its corresponding angle.
to solve the system of equations below, grace isolated the variable y in the first equation and then substituted into the second equation. what was the resulting equation? 3y=12x x^2/4+y^2/9=1
Answer:
The resulting equation is
x^2/4+16x^2/9=1
Step-by-step explanation:
The given equations are:
3y=12x eq(1)
x^2/4+y^2/9=1 eq(2)
We need to isolate variable y in equation 1
Divide both sides of the equation with 3
3y/3 = 12x/3
y = 4x
Now, substitute the value of y=4x in second equation
x^2/4+y^2/9=1
x^2/4 + (4x)^2/9 = 1
The resulting equation is
x^2/4+16x^2/9=1
Answer:
[tex]\frac{x^2}{4}+\frac{(4x)^2}{9}=1[/tex]
Step-by-step explanation:
Given system of equations,
[tex]3y=12x-----(1)[/tex]
[tex]\frac{x^2}{4}+\frac{y^2}{9}=1----(2)[/tex]
As per statement,
Isolating the variable y in the first equation,
[tex]y=\frac{12}{3}x=4[/tex]
Now, substituting into the second equation,
[tex]\frac{x^2}{4}+\frac{(4x)^2}{9}=1[/tex]
Which is the resulting equation,
Simplifying the equation,
[tex]\frac{x^2}{4}+\frac{16x^2}{9}=1[/tex]
[tex]\frac{9x^2+64x^2}{36}=1[/tex]
[tex]73x^2=36[/tex]
PLEASE HELP!!!
Point A, located at (-2, 4), is translated down 6 units. What are the coordinates of A'?
(-8, 4)
(-8, -2)
(-2, -2)
(-2, 4)
Point B, located at (-4, -7), is reflected over the y-axis. What are the coordinates of B'?
(-4, 7)
(4, -7)
(4, 7)
(-4, -7)
Answer for A. (-8,-2)
answer for B. (4,-7)
A right triangle has a hypotenuse that measures 42 feet and a length of another side of 31 feet. How long is the third side of the triangle?
Step-by-step explanation:
Use Pythagorean theorem:
c² = a² + b²
Here, c = 42 and a = 31.
42² = 31² + b²
b = √803
b ≈ 28.3
sally has a pet snail that fell into a well the well is 16 feet deep each day the snail climbs up 5 feet but each night it slides back diown 4 feet how many days will it take for sallys snail to get to the top of the well
Answer:
12 days
Step-by-step explanation:
Sally has pet snail that fell into a well.
Depth of the well = 16 feet
Snail climbs up 5 feet but each night it slides back down 4 feet.
So the snail climbs up per day = 5 feet - 4 feet = 1 feet.
Number of days snail took to reach at 11 feet = 11 × 1 = 11 feet
Remaining distance to cover by the snail = 16 - 11 = 5 feet
Number of days to cover remaining 5 feet to reach the top of the well = 1 day
Therefore, snail will take 12 days to reach the top of the well.
Final answer:
The snail climbs up 5 feet and slides back 4 feet each day in a 16-foot deep well. With a net gain of 1 foot per day, the snail will escape on the 16th day after reaching the top without sliding back.
Explanation:
Sally's pet snail finds itself in a classic mathematical problem often associated with algebra and arithmetic sequences. The snail is attempting to escape a 16-foot deep well by climbing up 5 feet during the day and sliding back 4 feet each night. To determine how many days it will take for the snail to get out, we need to calculate the net progress made by the snail each day and then examine how this applies on the final day of the snail's ascent.
Each day, the snail makes a net gain of 1 foot (5 feet up during the day minus 4 feet down at night). After 15 days, the snail would have climbed 15 feet during the day. On the 16th day, the snail climbs up 5 feet and reaches the top of the well, coming out without sliding back down since it already reached the goal during daylight. Therefore, it will take the snail a total of 16 days to escape the well.
Determine the end behavior for function f(x)=-x^4+5x^3-3
Answer:
Step-by-step explanation:
The dominant term of this function is x^4. The graph of x^4 starts in Quadrant II and continues in Quadrant I.
If we have y = -x^4, the graph starts in Quadrant III and continues in Quadrant IV. This is the end behavior for f(x)=-x^4+5x^3-3.
f(x)=3x+5/x, what is f(a-2)
Replace x with the binomial a - 2.
f(a - 2) = [3(a - 2) + 5]/(a- 2)
f(a - 2) = [3a - 6 + 5]/(a - 2)
f(a - 2) = [3a - 1]/(a - 2)
f(a - 2) = (3a - 1)/(a - 2)
Done.
Compute the distance between the two points. (–3, 4) and (21, 11)
For this case we have that by definition, the distance between two points is given by:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]
We have the following points:
[tex](x_ {1}, y_ {1}): (- 3,4)\\(x_ {2}, y_ {2}) :( 21,11)[/tex]
We replace:
[tex]d = \sqrt {(21 - (- 3)) ^ 2+ (11-4) ^ 2}\\d = \sqrt {(21 + 3) ^ 2 + (11-4) ^ 2}\\d = \sqrt {(24) ^ 2 + (7) ^ 2}\\d = \sqrt {576 + 49}\\d = \sqrt {625}\\d = 25[/tex]
Thus, the distance between the two points is 25 units.
Answer:
25
Answer:
The distance is 25 units
Step-by-step explanation:
Points to remember
Distance formula
Length of a line segment with end points (x1, y1) and (x2, y2) is given by,
Distance = √[(x2 - x1)² + (y2 - y1)²]
To find the distance between given points
Here (x1, y1) = (-3, 4) and (x2, y2) = (21, 11)
Distance = √[(x2 - x1)² + (y2 - y1)²]
= √[(21 - -3)² + (11 - 4)²]
= √[(21 +3)² + (11 - 4)²]
= √[24² + 7²]
= √(576 + 49)
= √625
=25
Therefore the distance is 25 units
Given O below, if WX and YZ are congruent, what is the measure of
Answer:
C
Step-by-step explanation:
Since the angles at the centre subtended by the congruent arcs WX and YZ
Then ∠YOZ = ∠WOX = 103° → C
The measure of the angle YOZ is b°. Option c is correct.
In a circle arc WX and YZ are congruent. Than angle YOZ is to be determine.
Arc is defined as the circular curve or part of circle. Arc = angle * radius.
Here, arc WX = arc YZ
If arc is equal in a circle than angle sub tainted by this arc to center are also equal.
angle YOZ = angle WOX = 103°
Thus, the measure of the angle YOZ is 103°.
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What is f[g(7)] for the following functions?
f(x) = 3x2 − 4
g(x) = 2x − 5
A.) f[g(7)] = 9
B.) f[g(7)] = 143
C.) f[g(7)] = 239
D.) f[g(7)] = 281
Answer:
C
Step-by-step explanation:
To evaluate f(g(7)), substitute x = 7 into g(x), then substitute the result into f(x)
g(7) = (2 × 7) - 5 = 14 - 5 = 9, then
f(9) = 3(9)² - 4 = 243 - 4 = 239 → C
Option C is correct.
Composite function :Given functions are, [tex]f(x)=3x^{2} -4,g(x)=2x-5[/tex]
We have to find [tex]f(g(7))[/tex].
[tex]g(7)=2*7-5=14-5=9[/tex]
So that, [tex]f(g(7))=f(9)[/tex]
[tex]f(9)=3*(9)^{2}-4\\ \\f(9)=243-4=239\\\\f(g(7))=f(9)=239[/tex]
Learn more about the composite function here:
https://brainly.com/question/10687170