The function f(x) = -4(x+2)² - 12 can be rewritten in the form
f(x) = -4x² - 16x - 28.
Simplifying the function:
The concept used in this problem is expanding and simplifying an algebraic expression. We are given a quadratic function in a different form, and we need to rewrite it in standard form, which is in the form of f(x) = ax² + bx + c.
This involves expanding and simplifying the squared term and combining like terms. The process of expanding and simplifying an algebraic expression is a fundamental concept in algebra.
Here we have
f(x)= -4(x+2)²- 12
To rewrite the function f(x) = -4(x+2)² - 12 in form f(x) = ax² + bx + c
Expand the squared term and simplify the expression.
The steps are as follows:
f(x) = -4(x+2)² - 12 (original function)
f(x) = -4(x² + 4x + 4) - 12 (expand the squared term)
f(x) = -4x² - 16x - 16 - 12 (distribute the -4)
f(x) = -4x² - 16x - 28 (combine like terms)
Therefore,
The function f(x) = -4(x+2)² - 12 can be rewritten in the form
f(x) = -4x² - 16x - 28.
Learn more about Algebraic expression at
https://brainly.com/question/19030913
#SPJ1
Moussa and Anand own competing taxicab companies. Both cab companies charge a
one-time pickup fee for every ride, as well as a charge for each mile traveled. Moussa
charges a $3 pickup fee and $2.20 per mile. The table below represents what Anand's
company charges.
Anand's Taxicab Company
Miles (2) Total Cost (y)
10
$25
20
$48
30
$71
40
$94
Use the dropdown menu and answer-blank below to form a
true statement.
Anand's company charges
per mile than Moussa's
options are more/less
Anand's business charges $25 for a 10-mile ride, which is less than Moussa's overall expenses.
How to calculate Anand's expense per mile?In comparison to Moussa, Anand's business costs less per mile.
Let's examine why by contrasting the costs charged by the two businesses for a 10-mile trip:
With a $3 pick-up fee and $2.20 per mile,
Moussa's business costs a total of $3 + $2.20*10 = $25.
Less than Moussa's overall expense,
Anand's business charges $25 for a 10-mile ride.
For all other distances mentioned in the table, we can verify that Anand's business charges less per mile than Moussa's. Thus, it is accurate that
"Anand's company charges less per mile than Moussa's."
Learn more about the total cost here:
https://brainly.com/question/30355738
#SPJ1
Choose the intervals where the graph has a decreasing average rate of change.
When the x-values rise while the y-values fall, this is known as a declining pattern. So, as x increases from 3 to 6, the graph declines. When the point on the graph at the interval's left end is higher than the interval's right end, the average rate of change will be declining.
What is the graph's average rate?An indicator of how much the function changed on average per unit throughout that time is the graph's average rate. In the graph of the function, it is calculated from the slope of the straight line joining the interval's ends. So, by applying the average rate of change formula, the slope of a graphed function is calculated.
Hence divide the y-value change by the x-value change in order to determine the average rate of change. When analyzing changes in observable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.
To learn more about graph's average rate, visit:
https://brainly.com/question/17179711
#SPJ1
The complete question is:
Choose the intervals where the graph has a decreasing average rate of change. The graph is attached below:
x = 0 to x = 13
x = 3 to x = 6
x = 4 to x = 8
x = 6 to x = 10
Tell whether the three side measure will make a triangle or not.
1. 6 cm, 5 cm, 3 cm
2. 5 cm, 12 cm, 13 cm
3. 2 in, 3 in, 2 in
4. 2 cm, 4 cm, 1 cm
5. 6 cm, 8 cm, 10 cm
6. 1 in, 2 in, 1 in
7. 5 cm, 7 cm, 4 cm
8. 2 in, 2 in, 2 in
9. 1 in, 5 in, 3 in
10. 3 cm, 4 cm, 5 cm
Please explain why, also this is due for me tomorrow and I’ll mark you brainlist if you can help me pls
1) Not a triangle as According to the triangle inequality theorem ,2)Triangle. as According to the triangle inequality theorem , 3)Not a triangle. , 4)Not a triangle., 5)Triangle. , 6)Not a triangle., 7) Not a triangle., 8)Equilateral triangle. 9)Not a triangle 10) Triangle.
what is triangle ?
A triangle is a two-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry, and it is formed by connecting three non-collinear points. The sum of the angles in a triangle is always 180 degrees.
In the given question,
Not a triangle. (6 + 5 = 11 > 3)
Explanation: According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the third side. However, in this case, 6 + 5 is equal to 11, which is not greater than the third side of length 3.
Triangle. (5 + 12 > 13)
Explanation: The sum of the two smaller sides (5 and 12) is greater than the largest side (13), satisfying the triangle inequality theorem. Therefore, a triangle can be formed with these side lengths.
Not a triangle. (2 + 2 = 4 > 3)
Explanation: Similar to the first case, the sum of the two smaller sides (2 and 2) is equal to 4, which is not greater than the third side of length 3.
Not a triangle. (1 + 2 = 3 > 4)
Explanation: Again, the sum of the two smaller sides (1 and 2) is equal to 3, which is not greater than the third side of length 4.
Triangle. (6 + 8 > 10)
Explanation: The sum of the two smaller sides (6 and 8) is greater than the largest side (10), satisfying the triangle inequality theorem. Therefore, a triangle can be formed with these side lengths.
Not a triangle. (1 + 1 = 2 > 2)
Explanation: Similar to cases 1 and 3, the sum of the two smaller sides (1 and 1) is equal to 2, which is not greater than the third side of length 2.
Not a triangle. (4 + 5 = 9 > 7)
Explanation: In this case, the sum of the two smaller sides (4 and 5) is greater than 7, but the difference between the two larger sides (7 - 5) is smaller than the smallest side (4), violating the triangle inequality theorem.
Equilateral triangle. (All sides are equal)
Explanation: All sides are equal, satisfying the criteria for an equilateral triangle.
Not a triangle. (1 + 3 = 4 > 5)
Explanation: The sum of the two smaller sides (1 and 3) is greater than the largest side (5), but the difference between the two larger sides (5 - 3) is smaller than the smallest side (1), violating the triangle inequality theorem.
Triangle. (3 + 4 > 5)
Explanation: The sum of the two smaller sides (3 and 4) is greater than the largest side (5), satisfying the triangle inequality theorem. Therefore, a triangle can be formed with these side lengths.
To know more about triangle , visit:
https://brainly.com/question/2773823
#SPJ1
A large toy top is a cone with a slant height of
10
cm
and radius of
6
cm
. The handle of the toy top is a cylinder with a diameter of
2
cm
and height
2
cm
. Determine the approximate volume of the top. Use
π
≈
3.14
.
For the given cone, the approximate volume of the toy top is 106.81 cubic centimeters. The three dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex.
What is volume?Volume is a three-dimensional quantity that measures the amount of space occupied by an object or a region in space.
The volume of the toy top can be calculated by finding the volumes of the cone and cylinder and then adding them together.
The volume of the cone is given by the formula V = (1/3)π[tex]r^{2}[/tex]h, where r is the radius and h is the height of the cone. In this case, the slant height is given, so we need to use the Pythagorean theorem to find the height:
h = [tex]\sqrt{(l^2 - r^2)[/tex] = [tex]\sqrt{(10^2 - 6^2)[/tex] = √(64) = 8 cm
Therefore, the volume of the cone is:
V_cone = (1/3)π[tex]r^2[/tex]h = (1/3)π([tex]6^2[/tex])(8) ≈ 100.53 [tex]cm^3[/tex]
The volume of the cylinder is given by the formula V = π[tex]r^2[/tex]h, where r is the radius and h is the height of the cylinder. In this case, the diameter is given, so we need to divide by 2 to get the radius:
V_cone = (1/3)πh = (1/3)πr = d/2 = 1 cm = 2 cm
Therefore, the volume of the cylinder is:
V_cylinder = π[tex]r^{2}[/tex]h = π([tex]1^{2}[/tex])(2) ≈ 6.28
The total volume of the toy top is:
V = V_cone + V_cylinder ≈ 100.53 + 6.28 ≈ 106.81 T
Therefore, the approximate volume of the toy top is 106.81 cubic centimeters.
To know more about cone, visit
brainly.com/question/1082469
#SPJ1
You leave your house to go the mall. You drive due north 8 miles, due east 7.5 miles, and due north again 2 miles. Answer b and c.
Answer:
CD = 1.5 milesAE = 12.5 milesStep-by-step explanation:
Given the figure with triangle ABC similar to triangle EDC and AB=8 mi, ED=2 mi, BD = 7.5 mi, you want the measures of CD and AE.
b. CDSimilar triangles will have corresponding sides proportional. That means ...
ED/CD = AB/CB
2/CD = 8/(7.5 -CD)
Inverting the ratios and multiplying by 8 gives ...
4·CD = 7.5 -CD
5·CD = 7.5 . . . . . . . add CD
CD = 1.5 . . . . . . . . . divide by 5
c. AEThe distance AE is the hypotenuse of a right triangle with side lengths 7.5 and (8+2) = 10. The Pythagorean theorem can be used to find AE:
AE² = 7.5² +10² = 56.25 +100 = 156.25
AE = √156.25 = 12.5
AE = 12.5 miles, the distance to the mall.
__
Additional comment
You may recognize these triangles are 3-4-5 triangles. ABC has a scale factor of 2, so has side lengths 6-8-10. EDC has a scale factor of 1/2, so has side lengths 1.5, 2, 2.5. The triangle with AE as its hypotenuse is the sum of these, so has a scale factor of 2.5 (miles).
AE = (2.5 miles) · 5 = 12.5 miles
The wholesale price for a chair is $181. A certain furniture store marks of the wholesale price by 22%. Find the price of the chair in the furniture store. Round your answer to the nearest cent as necessary.
To find the price of the chair in the furniture store, we need to calculate the retail price, which is the wholesale price plus the markup. The markup is calculated by multiplying the wholesale price by the markup rate as a decimal:
markup = 0.22 x $181 = $39.82
So the retail price is:
$181 + $39.82 = $220.82
Rounding to the nearest cent, we get the final answer:
The price of the chair in the furniture store is $220.82.
select all values for b that make the equation 8(x - 3) = 2x + b + 6x have no solutions for x. -24 -3 3 24
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{B (-3), C (3), and D (24)}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{8(x - 3) = 2x + b + 6x}[/tex]
Find: [tex]\textsf{Which values for b are not a solution}[/tex]
Solution: In order to make it easier for us to determine the answer, let us first simplify the expression that was given to us. We can do that by first combining like terms on the right side of the equation and distributing the 8 on the left side of the equation.
[tex]\textsf{8(x - 3) = 2x + b + 6x}[/tex][tex]\textsf{(8 * x) + (8 * -3) = 8x + b}[/tex][tex]\textsf{8x - 24 = 8x + b}[/tex]We can now subtract 8x from both sides of the equation.
[tex]\textsf{8x - 8x - 24 = 8x - 8x + b}[/tex][tex]\textsf{-24 = b}[/tex]Now that we know that b is equal to -24, that means that any value other than -24 would cause the equation to have no solutions. Therefore, the correct answer would be B (-3), C (3), and D (24).
Sixty-nine percent of U.S. college graduates expect stay at their first employer for three or more years. You randomly select 18 U.S. college graduates and ask them whether they expect to stay at their first employer for three or more years. Find the probability that the number who expect to stay at their first employer for three or more years is (a) than at least 15. Identify any unusual events. Explain
P(X >= 15) ≈ 0.271 is an unusual event would be one that has a very low probability of occurring (e.g., less than 5%).
What is probability?
Probability is a numerical measurement that represents the likelihood or chance of an event happening. The value of probability always lies between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.
a) To find the probability that at least 15 out of 18 U.S. college graduates expect to stay at their first employer for three or more years, we can also use the CDF of the binomial distribution:
P(X >= 15) = 1 - P(X < 15)
Using a calculator or statistical software, we find:
P(X >= 15) ≈ 0.271
An unusual event would be one that has a very low probability of occurring (e.g., less than 5%). Therefore, these outcomes could be considered unusual.
To learn more about probability visit:
https://brainly.com/question/24756209
#SPJ1
A table titled dice rolls has 7 rows and 2 columns. In the top row, result is in the first column and number of rolls is in the second column. In the second row, 1 is in the first column and 15 is in the second column. In the third row, 2 is in the first column and 18 is in the second column. In the fourth row, 3 is in the first column and 14 is in the second column. In the fifth row, 4 is in the first column and 16 is in the second column. In the sixth row, 5 is in the first column and 19 is in the second column. In the seventh row, 6 is in the first column and 18 is in the second column.
To find the average result of rolling a six-sided dice, Josh rolls a dice 100 times.
The table shows how many times Josh rolled each number. What is the mean,
or average, of the dice rolls?
Answer:16.7
Step-by-step explanation: So the first step is to add all of the numbers in the second column. (15,18,14,16,19,18). At the end of your problem it says 100. So you have 6 different numbers, and 100. You will do 100 divided by 6. Finally you will get 16.66 and you will just round it.
Multiply the following to put them in standard form
-4 (5x-2)=
Answer:
-2x × 10^1 + 8 × 10^0
or
-2x × 10 + 8 × 1
Step-by-step explanation:
Multiply the following to put them in standard form
-4 (5x-2)=
-20x +8
standard form
-2x × 10^1 + 8 × 10^0
or
-2x × 10 + 8 × 1 (remember PEMDAS)
Match each exercise with the first step needed to perform the operation. Do not actually perform the operation.
Choose the correct answer below.
A. Multiply the numerators and multiply the denominators.
B. Multiply the first rational expression by the reciprocal of the second rational expression.
C. Subtract the numerators. Place the difference over a common denominator.
D. Subtract the denominators. Place the difference below a common numerator.
what is the quotient? x^2-9 / x+3
Answer:
x-3
Step-by-step explanation:
On the first
day there were 4 laborers getting time and a half and 20 who were not for a total of $2080. On the
second day there were 2 laborers getting time and a half and 15 who were not for a total of $1440.
How much were the time and a half workers getting per day compared to the laborers who did not get
time and a half.
Answer:
"time and a half" workers were paid 50% more per day
Step-by-step explanation:
You want to know the relative daily pay rates of laborers making time and a half versus those who were not. 4 getting time and a half and 20 not earned a total of $2080, while 2 getting time and a half and 15 not earned a total of $1440.
SetupWe can let x and y represent the daily pay of time and a half workers, and those not earning time and a half. The two payrolls can be described by ...
4x +20y = 2080
2x +15y = 1440
SolutionSubtracting the first equation from 2 times the second, we have ...
2(2x +15y) -(4x +20y) = 2(1440) -(2080)
10y = 800 . . . . . . . simplify
y = 80 . . . . . . . . . . divide by 10
2x +15(80) = 1440
2x = 240 . . . . . . . . . . subtract 1200
x = 120 . . . . . . . . divide by 2
Workers getting time and a half made $120 per day; workers not getting time and a half made $80 per day. Workers getting time and a half made half again as much as those who didn't: $40 per day more, or 50% more, or half-again as much.
__
Additional comment
"Time and a half" means the pay is 50% more. That's what we see here. You don't need any math to say those getting time and a half were getting 50% more per day.
can you always divide by e^x? and what example can you give to prove this statement
Answer: No, you cannot always divide by e^x. When e^x equals zero, dividing by it would result in an undefined value or division by zero error.
For example, consider the function f(x) = e^x. We know that e^x is never equal to zero for any value of x. Therefore, we can always divide by e^x for any value of x, and the resulting quotient will be well-defined.
However, if we consider the function g(x) = 1 / e^x, we cannot always divide by e^x. When e^x equals zero, g(x) will be undefined. In fact, there is no value of x for which e^x is equal to zero, so the function g(x) is well-defined for all values of x.
In summary, dividing by e^x is allowed for most cases, except when e^x equals zero.
Step-by-step explanation:
A particle moves along the x-axis with velocity given by v(t) = 6t² + 8t - 5
for time t≥ 0. If the particle is at position x = -2 at time t = 2, what is
the position of the particle at time t = 1?
The position of the particle at time t = 1 would be -1.
Position of a particle at a time, tTo find the position of the particle at time t = 1, we need to integrate the velocity function v(t) from t = 0 to t = 1, and add it to the initial position x = -2:
x(1) = -2 + ∫[0,1] v(t) dt
Integrating v(t), we get:
x(1) = -2 + ∫[0,1] (6t² + 8t - 5) dt
x(1) = -2 + [2t³ + 4t² - 5t] from 0 to 1
x(1) = -2 + [2(1)³ + 4(1)² - 5(1)] - [2(0)³ + 4(0)² - 5(0)]
x(1) = -2 + [2 + 4 - 5]
x(1) = -2 + 1
x(1) = -1
Therefore, the position of the particle at time t = 1 is -1.
More on particle position can be found here: https://brainly.com/question/29187130
#SPJ1
A system of inequalities is shown. The graph shows a dashed upward opening parabola with a vertex at negative 2 comma negative 6, with shading inside the parabola. It also shows a dashed line passing through the points negative 3 comma negative 5 and 0 comma 4, with shading below the line. Which system is represented in the graph? y < x2 + 4x – 2 y > 3x + 4 y > x2 + 4x – 2 y < 3x + 4 y ≤ x2 + 4x – 2 y ≥ 3x + 4 y > x2 + 4x – 2 y > 3x + 4
Answer:
y > x² – 2x – 3
y > 3x + 4
Step-by-step explanation:
I took the test;. hoped this help.
i need help please
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
(A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
What is the rate of change?
The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.
A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.
Using the formula for an annual rate of change (r):
final value = initial value * [tex](1 - r)^t[/tex]
where t is the number of years and r is the annual rate of change expressed as a decimal.
Substituting the given values, we get:
$15,000 = $44,000 * (1 - r)¹⁴
Solving for r, we get:
r = 0.0804
So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.
B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:
r = 0.0804 * 100% = 8.04%
C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.
Substituting the known values, we get:
value in 2009 = $15,000 * (1 - 0.0804)³
value in 2009 = $11,628.40
Rounding to the nearest $50, we get:
value in 2009 = $11,650
Hence, (A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
To learn more about the rate of change visit:
https://brainly.com/question/29504549
#SPJ1
Solve the systems by graphing.
y =x+3
y = -2x - 6
Answer: (-3, 0)
Step-by-step explanation:
First, we will graph these equations. See attached. One has a y-intercept of 3 and then moves right one unit for every up down (we get this from the slope of 1). The other has a y-intercept of 4, and then moves down two units for every unit right (we get this from the slope of 1).
The point of intersection is the solution, this is the point at which both graphed lines cross each other. Our solution is:
(-3, 0) x = -3, y = 0
Answer:
(-3, 0)
Step-by-step explanation:
When we graph the equations:
y = x + 3,
y = -2 - 6,
we can see that they intersect at (-3, 0).
Therefore, that is the solution to the system.
— Extra note —
When graphing a line from a slope-intercept form equation (y = mx + b), we know the following:
m is the line's slope (rise over run)
b is the y-coordinate of the line's y-intercept
307200/100 in decimal form
Answer:
Step-by-step explanation:
divide both by 100 to get
3072/1
answer: 3072
calculate the area of the shaded region. the apothem is 2 ft, and the shaded area is 110 degrees. the figure is a circle.
The area of the shaded region is 1.916 ft²
What is Area?Area is a measure of the amount of space inside a two-dimensional shape, such as a square, rectangle, triangle, circle, or any other shape that has a length and a width. It is usually measured in square units, such as square inches, square feet, or square meters.
To calculate the area of the shaded region, we need to find the area of the entire circle and subtract the area of the unshaded portion.
The central angle corresponding to the shaded region is 110 degrees. The entire circle has a central angle of 360 degrees.
The unshaded portion of the circle is the sector that corresponds to the central angle of 360 - 110 = 250 degrees. The area of a sector of a circle with radius r and central angle θ is given by the formula:
A = (θ/360)πr²
Substituting θ = 110 degrees and r = 2 ft, we get:
A = (110/360)π(2)
A = (0.305)π(2)
A = (0.305)π(2)
A = 0.61π
A = 1.916 ft²
Therefore, the area of the shaded region is 1.916 ft².
To learn more about Area from given link.
https://brainly.com/question/12187609
#SPJ1
Complete question:
Calculate the area of the shaded region. the apothem is 2 ft, and the shaded area is 110 degrees. the figure is a circle
39÷63=? in simplest form as proper fraction
Answer:
[tex]\frac{13}{21}[/tex]
Hope this helps!
Step-by-step explanation:
[tex]\frac{39}{63}[/tex] ( Simplify both numerator and denominator by 3 )
39 ÷ 3 / 63 ÷ 3
[tex]\frac{13}{21}[/tex]
In a large population, 58 % of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.98693
If 58% = 58÷100 of the people have been vaccinated, then;
1 - (58/100) = 42% = 42÷100 of the people who have not been vaccinated.
Now:
Probability, P( > 1 ), that at least one of the selected four has been vaccinated is given by;
P( > 1 ) = 1 - P(0) -----------(1)
Where;
P(0) = probability that all of the four have not been vaccinated.
P(0) = P(1) x P(2) x P(3) x P(4)×p(5)
Where;
P(1) = Probability that the first out of the four has not been vaccinated
P(2) = Probability that the second out of the four has not been vaccinated
P(3) = Probability that the third out of the four has not been vaccinated
P(4) = Probability that the fourth out of the four has not been vaccinated
P(5)=Probability that the fifth out of the five has not been vaccinated
Remember that 42÷100 of the population has not been vaccinated. Therefore,
P(1) = 42÷100
P(2) = 42÷100
P(3) = 42÷100
P(4) = 42÷100
P(5)=42÷100
P(0) = (42÷100) x (42÷100) x (42÷100) x (42÷100)×(42÷100)
P(0) = (42÷100)⁵
P(0) = (0.42)⁵
P(0) = 0.013067
Therefore, from equation (1);
P( > 1 ) = 1 -0.013067
P( > 1 ) = 0.98693
Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.98693
learn more about Probability,
https://brainly.com/question/11234923
#SPJ1
98+x=154
x-4=20
x+25=-10
Answer:
98+x=154
x=154-98
x=56
x-4=20
x=20+4
x=24
x+25=-10
x=-10-25
x=-35
Solve a triangle with b =7, c =10, and A= 51. round to the nearest tenth
The sides of the triangle are a ≈ 8.3, b = 7, and c = 10, and the angles are A = 51°, B ≈ 51.5°, and C ≈ 77.5°.
What is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles.
To solve the triangle, we need to find the values of the remaining sides and angles. We can start by using the Law of Sines, which states that:
a / sin A = b / sin B = c / sin C
where a, b, and c are the sides of the triangle, and A, B, and C are the angles opposite to those sides.
Using the given values, we can write:
a / sin 51 = 7 / sin B
a / sin 51 = 10 / sin C
To solve for a, we can use either of the two equations above. Let's use the first one and solve for sin B:
sin B = (7 / sin 51) * sin B
sin B = 7 / (sin 51 / sin B)
sin B = 7 / sin(180 - 51 - B)
sin B = 7 / sin(129 - B)
Using the sine rule, we can determine the angle B:
sin B / 7 = sin(129 - B) / 10
sin B = (7/10) * sin(129 - B)
sin B = (7/10) * (sin 129 * cos B - cos 129 * sin B)
sin B = (7/10) * sin 129 * cos B - (7/10) * cos 129 * sin B
(7/10 + (7/10) * cos 129) * sin B = (7/10) * sin 129 * cos B
sin B = (7/10) * sin 129 * cos B / (7/10 + (7/10) * cos 129)
sin B = sin 51.5
B = sin(sin B)
B = sin(sin 51.5)
B ≈ 51.5°
We can now find the remaining angle, C:
C = 180 - A - B
C = 180 - 51 - 51.5
C ≈ 77.5°
Finally, we can use the Law of Sines again to find the remaining side, a:
a / sin A = c / sin C
a / sin 51 = 10 / sin 77.5
a = (10 * sin 51) / sin 77.5
a ≈ 8.3
Therefore, the sides of the triangle are a ≈ 8.3, b = 7, and c = 10, and the angles are A = 51°, B ≈ 51.5°, and C ≈ 77.5°.
To know more about triangle visit:
brainly.com/question/2773823
#SPJ1
Victor is using the distributive property on the expression 9-4(5x-6) Here is his work:
9-4(5x-6)
9+(4)(5x+-6)
9+-20x+-6
3-20x
a. Find the step where victor made an error and explain what he did wrong
b. Correct victor's work
Answer:
33 - 24x
Step-by-step explanation:
a. He made mistake here
9+(4)(5x+-6)
b.
9 - 4(5x - 6)
= 9 + (- 4)(5x - 6)
= 9 + (- 4)(5x) - (- 4)(6)
= 9 + (- 20x) - (- 24)
= 9 - 20x + 24
= 9 + 24 - 24x
= 33 - 24x
Determine the equation of the circle with center (-6, -2 containing the point (-9, -2).
The equatiοn οf the circle is (x + 6)(x+6) + (y + 2)(y+2) = 9.
What is circle ?A circle is a twο-dimensiοnal geοmetric figure that cοnsists οf all pοints that are equidistant frοm a single fixed pοint called the center. A circle can alsο be defined as the lοcus οf a pοint that mοves in a plane in such a way that its distance frοm a fixed pοint is always cοnstant.
Tο find the equatiοn οf a circle, we need the cοοrdinates οf the center and the radius.
The center οf the circle is given as (-6, -2), sο the cοοrdinates οf the center are (h, k) = (-6, -2).
The pοint (-9, -2) is οn the circle, sο its distance frοm the centre is equal tο the radius. We can use the distance fοrmula tο find the radius:
[tex]\rm r = \sqrt{((x_2 - x_1)\times (x_2 - x1) + (y_2 - y_1)\times(y_2 - y_1))}[/tex]
[tex]= \sqrt{((-3)^2 + 0^2)[/tex]
= 3
Therefοre, the radius οf the circle is 3.
Nοw we can use the standard fοrm οf the equatiοn οf a circle, which is:
(x - h)(x-h)+ (y - k)(y-k)= r*r
Substituting the values we fοund, we get:
Simplifying:
(x + 6)(x+6) + (y + 2)(y+2) = 9
Therefοre, The equatiοn οf the circle is [tex](x + 6)(x+6) + (y + 2)(y+2) = 9[/tex].
To learn more about Circle from given link.
https://brainly.com/question/266951
#SPJ1
Two same-sized triangular prisms are attached to a rectangular prism as shown below.
If a = 20 cm, b = 13 cm, c = 12 cm, d = 5 cm, and e = 8 cm, what is the surface area of the figure?
Answer:1,208 square centimeters
Step-by-step explanation:
what is p(divisor of 6) write your answer as a percentage rounded to the nearest tenth
The probability of selecting a divisor of 6 is 66.7%.
What is probability?It is expressed as a number between 0 and 1, where 0 represents an impossible event (it will never occur) and 1 represents a certain event (it will always occur).
According to question:1, 2, 3, and 6 can be divided by 6.
To find the probability (p) of selecting a divisor of 6, we need to divide the number of divisors of 6 by the total number of possible outcomes, which is also 6 (since there are 6 positive integers from 1 to 6).
So, p(divisor of 6) = number of divisors of 6 / total number of outcomes
= 4 / 6
= 2 / 3
We can multiply this fraction by 100 to get the percentage:
p(divisor of 6) = 2 / 3 * 100
= 66.7%
Rounded to the nearest tenth, the answer is 66.7%. Therefore, the probability of selecting a divisor of 6 is 66.7%.
To know more about probability visit:
https://brainly.com/question/29221515
#SPJ1
PLEASE HELP ASAP!!! THANKS
Answer: 28/52
Step-by-step explanation: its easy
Answer:
28/52. You will get it right.
A report on consumer financial literacy summarized data from a representative sample of 1,669 adult Americans. When asked if they typically carry credit card debt from month to month, 587 of these people responded "yes." Estimate p, the proportion of adult Americans who carry credit card debt from month to month. (Round your answer to three decimal places.)
The answer is 0.351
To estimate the proportion p of American adults with monthly credit card debt, the sample proportion can be used as an estimate. The sample ratio is simply the number of people in the sample with monthly credit card debt divided by the total number of people in the sample.
p hat = 587/1669
p-hat = 0.3511 (rounded to four decimal places)
Therefore, based on this sample, the percentage of adult Americans with monthly credit card debt is estimated to be approximately 0.351. After rounding to three decimal places, its estimate is 0.351.
To know more about proportion visit : https://brainly.com/question/30657439
#SPJ1