Answers
Answer:
Correct: A, D, F
Step-by-step explanation:
Consider right triangle EFG.
By the definition of the cosine function,
[tex]\cos \angle E=\dfrac{EG}{EF}\\ \\\cos 30^{\circ}=\dfrac{EG}{EF}\\ \\\dfrac{\sqrt{3}}{2}=\dfrac{EG}{EF}\\ \\EG=\dfrac{\sqrt{3}}{2}EF[/tex]
Option F is correct.
By the definition of the sine function,
[tex]\sin \angle E=\dfrac{FG}{EF}\\ \\\sin 30^{\circ}=\dfrac{GF}{EF}\\ \\\dfrac{1}{2}=\dfrac{GF}{EF}\\ \\GF=\dfrac{1}{2}EF\\ \\EF=2FG[/tex]
Option D is correct.
By the definition of tangence,
[tex]\tan \angle E=\dfrac{FG}{EG}\\ \\\tan 30^{\circ}=\dfrac{GF}{EGF}\\ \\\dfrac{1}{\sqrt{3}}=\dfrac{GF}{EG}\\ \\GF=\dfrac{1}{\sqrt{3}}EGF\\ \\EG=\sqrt{3}FG[/tex]
Option A is correct
Related Questions
Question 1 Post Math
Answers
ANSWER
Yes, k=-3 and y=-3x
EXPLANATION
Let's assume y varies directly as x.
Then, we can write the equation:
y=kx
From the table, when x=1, y=3
Substitute these values to obtain;
3=-k
This implies
k=-3
The equation now becomes:
y=-3x
We check for a second point to see if it satisfy the equation.
When x=5,y=-15
-15=-3(5)
-15=-15
Hence the relation represent a direct variation.
which is more 45g or 45ml?
Answers
For water 1 gram = 1 ml.
This means 45 grams are equal to 45 ml's.
Neither one is greater than the other one as they are equal.
The problem doesn't state what is being measured, so the answer could be different depending on the density of the product being measured.
A quadratic equation has the zeros -3 amd 6. Can the quadratic equation be the given equation? A. (2x + 6)(x - 6) =0. Yes or no B. (6x - 1)(x + 3) =0. Yes or no C. -3x(x - 6) =0. Yes or no
Answers
Answer:
It can be A. (not B or C)
Step-by-step explanation:
It is A because x-6=0 can be simplified to x=6. Then, 2x + 6, you can divide the whole equation resulting in x+3=0, simplify this and you get x=-3. YES
It is not B because, while x+3=0 results in a zero of -3, 6x-1 can be simplified to be divided by 6. When we do this we get x-1/6=0, which is not equivalent to 6. NO
It is not C because, while x-6=0 results in a zero of 6, -3x can be simplified with the zero product property to get -3x=0 then dividing -3 by 0 giving you 0 which is not equivalent to one. NO
A jar contains only black and white marbles. When one marble is drawn at random, the probability that it is white is 1/3. After 20 black marbles were added to the jar, the probability of drawing a white was 1/5. How many marbles were in the jar originally?
Answers
there are 30 marbles in the jar originally
On Orca Beach, the high tide is 2 meters and only occurs at 12 a.m. and 12 p.m. The low tide is 0.8 meter and only occurs at 6 a.m. and 6 p.m. Which function models the height of the tide t hours after 12 a.m.?
Choices:
1. h(t)=2cos(πt/3)+0.8
2. h(t)=0.6cos (πt/6) + 1.4
3. 0.6sin(πt/6) + 1.4
4. 1.4sin (πt/3) + 2
Answers
Answer:
2. h(t)=0.6cos (πt/6) + 1.4
Step-by-step explanation:
The average water level is (2 +0.8)/2 = 1.4, so this is the offset that is added to the sine or cosine function. That eliminates choices 1 and 4.
The high tide occurs when t=0 (at 12 AM), so eliminating choice 3.
The function that models the height of the tide t hours after 12 AM is ...
h(t)=0.6cos (πt/6) + 1.4
Final answer:
The height of the tide t hours after 12 a.m. at Orca Beach can be modeled by the function h(t)=0.6cos(πt/6)+1.4, which is choice 2 among the given options. This function correctly represents the amplitude and timing of the high and low tides with the period of 12 hours between each high tide.
Explanation:
The question is asking to find a function that models the height of the tide at Orca Beach t hours after 12 a.m. Given that the high tide of 2 meters occurs at 12 a.m. and 12 p.m., and the low tide of 0.8 meter occurs at 6 a.m. and 6 p.m., we're looking for a trigonometric function with a period that corresponds to the tidal cycle of 12 hours. The amplitude of the tide would be half the difference between the high and low tides, and the vertical shift would position the midline of the oscillation at the average of the high and low tides.
First, we calculate the amplitude (A) as half the difference between the high and low tide heights:
A = (2 - 0.8) / 2 = 0.6 meters
Next, we calculate the vertical shift (D) as the average of the high and low tide heights:
D = (2 + 0.8) / 2 = 1.4 meters
Now, knowing that the period (T) of the tide is 12 hours, we can use the cosine function, as it starts at the maximum value at t=0, corresponding to the high tide at 12 a.m. The function representing the tide's height h(t) can be modeled as:
h(t)=Acos(Bt)+D
Where B is the frequency, calculated as B = 2π / T.
Since the tide has a 12-hour period, we plug T = 12 into B:
B = 2π / 12 = π / 6
So the function that models the height of the tide t hours after 12 a.m. with the correct amplitude, frequency, and vertical shift is:
h(t)=0.6cos(πt/6)+1.4
Therefore, the correct choice from the options provided is:
Choice 2: h(t)=0.6cos (πt/6) + 1.4
What is the absolute deviation for 15 in the data set?
{20, 20, 30, 15, 40}
A. 5
B. 10
C. 15
D. 25
Answers
Final answer:
The absolute deviation of 15 in the data set {20, 20, 30, 15, 40} is the absolute value of (15 minus the mean 25), which is 10. So, the correct answer is B. 10.
Explanation:
To calculate the absolute deviation of a number in a data set, you subtract the number from the mean of the data set and take the absolute value of the result. The mean of the data set {20, 20, 30, 15, 40} is (20 + 20 + 30 + 15 + 40) / 5, which equals 125 / 5 or 25. The absolute deviation for the number 15 would be the absolute value of (15 - 25), which is the absolute value of -10 or simply 10. Therefore, the correct answer is B. 10.
Look at the two circles below . They share a center point . The larger circle has a radius of 10 inches . The distance between the smaller circle and the larger circle is 2 inches . Which best represents the shaded area between the two circles
Answers
Answer:
π(10 in)² - π(8 in)²
Step-by-step explanation:
Area between the two circles=
Area of larger circle less area of smaller circle, or
π(10 in)² - π(8 in)² Since the difference in the radii of the
two circles is 2, that means the smaller
circle has radius 10 - 2, or 8 (inches)
Next time, please share the answer choices. Thank you.
To find the shaded area between the two circles, subtract the area of the smaller circle from the area of the larger circle. The area of a circle is calculated using the formula A = πr^2. By finding the radius of the smaller circle, we can calculate its area and subtract from the larger circle's area to find the shaded area.
Explanation:The shaded area between the two circles can be found by subtracting the area of the smaller circle from the area of the larger circle. The radius of the larger circle is given as 10 inches and the distance between the two circles is given as 2 inches. To find the area of the shaded region, we first need to find the radius of the smaller circle. Since the distance between the two circles is equal to the sum of their radii, the radius of the smaller circle is 10 inches - 2 inches = 8 inches.
The area of the larger circle is calculated using the formula A = πr^2, where r is the radius. Therefore, the area of the larger circle is A = π(10 inches)^2 = 100π square inches.
The area of the smaller circle is calculated in the same way, using the radius of 8 inches. Therefore, the area of the smaller circle is A = π(8 inches)^2 = 64π square inches.
To find the shaded area, we subtract the area of the smaller circle from the area of the larger circle: 100π square inches - 64π square inches = 36π square inches.
In the game Yahtzee, players roll five dice. There are 13 rounds per game. In each round, each player can roll the dice up to three times. In a player's first roll of each round, he or she rolls all five dice. The second and third rolls, the player can choose to roll any subset of the dice again (any or all the dice). Yahtzee is a bit like poker with dice. An especially valuable roll is 5 of a kind (all 5 dice show the same number of spots), called a Yahtzee. The next two questions are about Yahtzee. Problem 3 The chance of rolling a Yahtzee (5 of a kind) on the first roll of a turn is closest to
Answers
Answer: 13
Step-by-step explanation: because I have the whole bookanswer duh
A runner runs around a track consisting of two parallel lines 96 m long connected at the ends by two semicircles with a radius of 49 m. She completes one lap in 100 seconds. What is her average velocity?
Answers
Answers:0m/s
Step-by-step explanation: once she has completed one lap, displacement is 0, therefore her velocity is 0m/s
The average velocity of her is zero.
Average velocity;Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs.
Given
A runner runs around a track consisting of two parallel lines 96 m long connected at the ends by two semicircles with a radius of 49 m.
She completes one lap in 100 seconds.
The formula is used to find average velocity is;
[tex]\rm Average \ velocity=\dfrac{Change \ in \ displacement }{Change \ in \ time \ interval}[/tex]
Here, the runner displacement is zero.
Therefore,
[tex]\rm Average \ velocity=\dfrac{Change \ in \ displacement }{Change \ in \ time \ interval}\\\\\rm Average \ velocity=\dfrac{0 }{100}\\\\\rm Average \ velocity=0[/tex]
Hence, the average velocity of her is zero.
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The statement tan theta -12/5, csc theta -13/12, and the terminal point determined by theta is in quadrant 2."
Answers
Answer is C. This is because in quadrant 2, [tex]\sin\theta>0[/tex] so [tex]\csc\theta>0[/tex] is also true.
Answer with explanation:
Let , Theta =A
[tex]\tan A=\frac{-12}{5}\\\\ \csc A=\frac{-13}{12}[/tex]
In First Quadrant all Trigonometric Function are Positive.
→In Quadrant,II , Sine and Cosecant , Function are Positive only.
→Cosecant theta is negative.So, Terminal point can't be in Second Quadrant.
Option C:
Find the exponential regression equation for the data points (-4, 0.75), (-2, 6), (3, 28), and (5, 162).
A. y = 8.43(1.69)^x
B. y = 9.17(1.70)^x
C. y = 5(0.92)^x
D. y = 9.46(2.93)^x
Answers
If im not wrong, i believe the answer is C.
Please help me out please
Answers
Answer:
∠ABD = 20°
Step-by-step explanation:
Since BD is the angle bisector of ∠ABC then
∠ABD = ∠DBC ← substitute values
3x - 1 = 34 - 2x ( add 2x to both sides )
5x - 1 = 34 ( add 1 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7
Hence
∠ABD = 3x - 1 = (3 × 7) - 1 = 21 - 1 = 20°
The profit a company earns every month depends of the amount of the product sold, p, for $855 each and the amount spent in rent,utilities and other expenses, which always totals to $6,780. The CEO of the company earns 15% of this profit. How much does the CEO earn if the company sells 250 products in a given month?
Answers
Answer:
$31,045.50
Step-by-step explanation:
Revenue from sales = ($855/item)p
Expenses: $6,780
Revenue if p = 250 is R(250) = ($855/item)(250 items) = $213,750
Subtracting expenses, we get a profit of $206,970.
The CEO of the company earns 15% of this profit, or:
0.15($206,970) = $31,045.50
In Exercises 10 and 11, points B and D are points of tangency. Find the value(s) of x.
Answers
In both cases,
[tex]AB^2=AD^2[/tex]
(as a consequence of the interesecting secant-tangent theorem)
So we have
10.
[tex](4x+7)^2=(6x-3)^2[/tex]
[tex]16x^2+56x+49=36x^2-36x+9[/tex]
[tex]20x^2-92x-40=0[/tex]
[tex]5x^2-23x-10=0[/tex]
[tex](5x+2)(x-5)=0\implies\boxed{x=5}[/tex]
(omit the negative solution because that would make at least one of AB or AD have negative length)
11.
[tex](4x^2-18x-10)^2=(x^2+x+4)^2[/tex]
[tex]16x^4-144x^3+244x^2+360x+100=x^4+2x^3+9x^2+8x+16[/tex]
[tex]15x^4-146x^3+235x^2+352x+84=0[/tex]
[tex](x-7)(3x+2)(5x^2-17x-6)=0\implies\boxed{x=-\dfrac23\text{ or }x=7}[/tex]
(again, omit the solutions that would give a negative length for either AB or AD)
The value of x for first figure is x = 5 and for second x = 7 and -2/3.
What is the property of tangent?The property of tangent is that "if two tangents from the same exterior point are tangent to a circle, then they are congruent".
1. The value of x using the above tangent property.
BA = AD
4x + 7 = 6x -3
4x - 6x = -3 -7
-2x = -10
x = -10/-2
x = 5
2. The value of x using the above tangent property.
BA = AD
[tex]\rm 4x^2-18x-10=x^2+x+4\\\\4x^2-18x-10-x^2-x-4=0\\\\3x^2-19x-14=0\\\\x =\dfrac{-(-19)\pm\sqrt{(-19)^2-4\times 3\times -14} }{2\times 3}\\\\x =\dfrac{19\pm\sqrt{361+168} }{6}\\\\x =\dfrac{19\pm\sqrt{529} }{6}\\\\x =\dfrac{19+23 }{6}, \ x =\dfrac{19-\ 23}{6}\\\\x =\dfrac{42}{6} , \ x =\dfrac{-4}{6}\\\\x=7, \ x=\dfrac{-2}{3}[/tex]
Hence, the value of x for first figure is x = 5 and for second x = 7 and -2/3.
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What is the maximum value of the equation y=-x^2 -x+6
1.) 1/2
2.)6 1/4
3.) -1/2
4.)5 1/4
Answers
Answer:
1) 1/2
Step-by-step explanation:
A triangle is graphed in the coordinate plane. The vertices of the triangle have coordinates (–3, 1), (1, 1), and (1, –2). What is the perimeter of the triangle?
Answers
Answer:
The perimeter of the triangle is [tex]12\ units[/tex]
Step-by-step explanation:
Let
[tex]A(-3,1),B(1,1),C(1,-2)[/tex]
we know that
The perimeter of triangle is equal to
[tex]P=AB+BC+AC[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance AB
[tex]A(-3,1),B(1,1)[/tex]
substitute in the formula
[tex]AB=\sqrt{(1-1)^{2}+(1+3)^{2}}[/tex]
[tex]AB=\sqrt{(0)^{2}+(4)^{2}}[/tex]
[tex]AB=4\ units[/tex]
step 2
Find the distance BC
[tex]B(1,1),C(1,-2)[/tex]
substitute in the formula
[tex]BC=\sqrt{(-2-1)^{2}+(1-1)^{2}}[/tex]
[tex]BC=\sqrt{(-3)^{2}+(0)^{2}}[/tex]
[tex]BC=3\ units[/tex]
step 3
Find the distance AC
[tex]A(-3,1),C(1,-2)[/tex]
substitute in the formula
[tex]AC=\sqrt{(-2-1)^{2}+(1+3)^{2}}[/tex]
[tex]AC=\sqrt{(-3)^{2}+(4)^{2}}[/tex]
[tex]AC=5\ units[/tex]
step 4
Find the perimeter
[tex]P=AB+BC+AC[/tex]
substitute the values
[tex]P=4+3+5=12\ units[/tex]
Enter the values for the highlighted variables that show how to subtract the rational expressions correctly:
Answers
Answer:
a = 6
x^2 + 6x is equal to x(x+6)
b=2
Denominator and numerator of the first term are multiplied by x.
c=6
Second term is multiplied by (x-6)/(x-6)
d=2
Now that they have the same denominator, the two terms are combined. 2 is the coefficient of the first term
e=6
In the same way as d is carried over from b, e is carried over from c.
f = 6
2x - x + 6 = x + 6
g = 1
We factor out the (x+6) from the numerator and denominator.
Answer:
a= 6
b= 2
c= 6
d= 2
e= 6
f= 6
g= 1
Step-by-step explanation:
i like math
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Answers
Answer:
C. Center (3,-2) and radius 3
Step-by-step explanation:
The given circle has equation:
[tex]x^2+y^2-6x+4y+4=0[/tex]
We rearrange to get:
[tex]x^2-6x+y^2+4y=-4[/tex]
We add the square of half the coefficients of the linear terms to both sides of the equation:
[tex]x^2-6x+(-3)^2+y^2+4y+(2)^2=-4+(-3)^2+(2)^2[/tex]
We factor the perfect squares and simplify to get;
[tex](x-3)^2+(y+2)^2=9[/tex]
We can rewrite as;
[tex](x-3)^2+(y--2)^2=3^2[/tex]
Comparing this to the standard equation of the circle;
[tex](x-h)^2+(y-k)^2==r^2[/tex]
We have (3,-2) and the center and r=3 as the radius.
Identify the diameter of the disc. HELP ASAP!!
Answers
Answer:
Its 9 1/16
Step-by-step explanation:
I guessed and got it right. I just knew it wasn't 9 and the two 16 answers didn't make sense, lol. In the future I think just go with the one closest (but not exact) to the shown thingy, not sure tho?
Update:
Im silly. Solve it like this:
AE*EB=CEtimesED
so 9 which is 4.5*2 would be 4.5*4.5
thats 20.25
20.25/4(the radius)
is 5.06.
That plus 4 is the diameter, lol.
so it rounds to 9 1/16
You need to repaint the floor and inside wall of your circular swimming pool. It has a diameter of 16 feet and a depth of 5 feet. What is the surface area that needs to be repainted? (Use 3.14 for π.)
1,055.04 ft 2
251.2 ft 2
401.92 ft 2
452.16 ft 2
Answers
Answer:
452.16 ft²
Step-by-step explanation:
The surface area is the area of the cylindrical wall plus the area of the circular floor.
A = 2πrh + πr²
h = 5. The radius is half the diameter, so r = 8.
A = 2π(8)(5) + π(8)²
A = 144π
A ≈ 452.16 ft²
Answer:
A ≈ 452.16 ft mark me brainy plz!
Step-by-step explanation:
The surface area is the area of the cylindrical wall plus the area of the circular floor.
A = 2πrh + πr²
h = 5. The radius is half the diameter, so r = 8.
A = 2π(8)(5) + π(8)²
A = 144π
A ≈ 452.16 ft²
question 70 true or false
Answers
Answer:
true
Step-by-step explanation:
For this case we have that by definition:
[tex]Sin (90) = 1\\Cos (90) = 0[/tex]
Now, the tangent of 90 is given by:
[tex]tg (90) = \frac {Sin (90)} {Cos {90}} = \frac {1} {0}[/tex]
Thus, it is observed that the tangent of 90 degrees is not defined. Is obtained ∞.
Similarly:
[tex]Sin (-90) = - 1\\Cos (-90) = 0[/tex]
Now, the tangent of -90 is given by:
[tex]tg (-90) = \frac {Sin (-90)} {Cos {-90}} = \frac {-1} {0}[/tex]
Thus, it is observed that the tangent of -90 degrees is not defined.
Answer:
False
Problem
An engineer is planning a new water pipe installation. The circular pipe has a diameter of d=20\text{ cm}d=20 cmd, equals, 20, space, c, m.
What is the area AAA of the circular cross section of this pipe?
Give your answer in terms of pi.
Answers
Answer:
The area of the circular cross section of the pipe is [tex]100\pi\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the circle (cross section of the pipe) is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=20/2=10\ cm[/tex] ----> the radius is half the diameter
substitute
[tex]A=\pi (10)^{2}[/tex]
[tex]A=100\pi\ cm^{2}[/tex]
Please please help me please
Answers
Answer:
x=8
Step-by-step explanation:
To solve this, we must use the Pythagorean theorem.
a=15, b=x, and c=17
[tex](15)^2 +b^2=(17)^2\\\\b=\sqrt{17^2-15^2} \\\\b=\sqrt{289-225} \\\\b=\sqrt{64} \\\\b=8[/tex]
a^2+b^2=c^2
In this case, 15=a and 17=c and if you substitute the variables as the numbers, you would get the equation 15^2+b^2=17^2. If you simplify that you would get 225+b^2=289. You subtract 225 from both sides and you get left with b^2=64. The square root of 64 is 8 so I’m this problem x is 8.
ANSWER~ 8
Troy is making a flag shaped like a square. Each side measures 12 inches. He wants to add ribbon along the edges. He has 36 inches of ribbon. Does he have enough ribbon?
Answers
Answer:
no he needs 12 more
Step-by-step explanation:
There are 17 people in an office with 5 different phone lines. If all the lines begin to ring at once, how many groups of 5 people can answer these lines?
Answers
Answer:
6188 different combinations of people
Step-by-step explanation:
This is a combination problem since it does not matter the order of people that answer the phones. The combination looks like this:
₁₇C₅ = [tex]\frac{17!}{5!(17-5)!}[/tex]
This expands to
[tex]\frac{17*16*15*14*13*12!}{5*4*3*2*1(12!)}[/tex]
The 12! cancels out in the top and bottom so the remaining multiplication leaves you with
₁₇C₅ = [tex]\frac{742560}{120}[/tex]
which divides to 6188
The number of groups of 5 people that can be selected from a total of 17 to answer 5 different phone lines is 6188. This is a combinatorics problem calculated using the combinations formula.
Explanation:The question is asking us to determine how many groups of 5 people out of 17 people can answer the 5 different phone lines in an office. This problem is a combination problem in mathematics, particularly in combinatorics. Combinations refer to the selection of items without regard for the order in which they are arranged.
Here, we are selecting groups of 5 people out of 17 to answer the phone lines. The formula for combinations is C(n, r) = n! / r!(n-r)!, where n is the total number of items, r is the items to be selected, and '!' denotes the factorial.
Substituting our values into the formula, we get C(17, 5) = 17! / 5!(17-5)!. When we calculate this, the answer we obtain is 6188. Therefore, there are 6188 ways to form groups of 5 out of 17 people to answer the phone lines.
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An office building has a cement block under its dumpster. The pad has an area of 108 square feet. The dumpster is 9 ft long and 8 ft wide. What is the most likely perimeter of the cement pad
Answers
Answer:
Most likely Perimeter of the pad is 42 ft.
Step-by-step explanation:
Area of the Cement pad = 108 feet²
Length of the dumpster = 9 ft
Width of the dumpster = 8 ft
Cement pad surface is greater than dumpster to hold it.
Area of pad = 108 ft²
length × width = 108
we choose length and width such that they are greater than length and width of the dumpster.
So, length of the pad = 12 ft
Width of the pad = 9 ft
Thus, Perimeter = 2 × (length + width) = 2 × ( 12 + 9 ) = 2 × 21 = 42 ft
Therefore, Most likely Perimeter of the pad is 42 ft.
Which second-degree polynomial function f (x) has a lead coefficient of 4 and roots 5 and 2?
Answers
Answer:
The second degree polynomial is f(x) = 4x² - 28x + 40
Step-by-step explanation:
* Lets revise the general form of the second-degree polynomial
- The general form of the second degree polynomial is
f(x) = ax² + bx + c, where a , b , c are constant
- The highest power of the variable that occurs in the polynomial
is called the degree of a polynomial.
- The leading term is the term with the highest power, and its
coefficient is called the leading coefficient.
- The leading coefficient is the coefficient of x²
∴ a = 4
∴ f(x) = 4x² + bx + c
- The roots of a polynomial are also called its zeroes, because
the roots are the x values at which the function equals zero
∴ When f(x) = 0, the values of x are 5 and 2
* To find the value of b and c substitute the values of x in f(x) = 0
- At x = 5
∵ 4(5)² + b(5) + c = 0 ⇒ simplify it
∴ 100 + 5b + c = 0 ⇒ subtract 100 from both sides
∴ 5b + c = -100 ⇒ (1)
- At x = 2
∵ 4(2)² + b(2) + c = 0 ⇒ simplify it
∴ 16 + 2b + c = 0 ⇒ subtract 16 from both sides
∴ 2b + c = -16 ⇒ (2)
- Subtract (2) from (1)
∴ 3b = -84 ⇒ divide both sides by 3
∴ b = -28
- Substitute the value of b in (1) or (2) to find c
∵ 2(-28) + c = -16
∴ -56 + c = -16 ⇒ add 56 to both sides
∴ c = 40
∴ f(x) = 4x² - 28x + 40
* The second degree polynomial is f(x) = 4x² - 28x + 40
Answer:
d
Step-by-step explanation:
Please help me with this:)
Answers
Answer: multiply all of them by two and then put the fx2 behind the equal signs in punuations =(fx2)
Step-by-step explanation:
Answer:
16 ft²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 8 and h = 4, thus
A = 0.5 × 8 × 4 = 16 ft²
A cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift. What is the approximate volume of the tube? Round to the nearest whole cubic centimeter. 1
Answers
if it has a diameter of 8 units, then its radius is half that, or 4.
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=20 \end{cases}\implies V=\pi (4)^2(20)\implies V=320\pi \\\\\\ V\approx 1005.309649148733\implies \stackrel{\textit{rounded up}}{V=1005}[/tex]
To calculate the volume of a cylindrical cardboard tube, the formula V = πr²h is used with a given diameter of 8 cm (radius of 4 cm) and a height of 20 cm. After computation, the approximate volume is 1005 cm³, rounded to the nearest whole number.
Explanation:To find the volume of the cylindrical cardboard tube, we need to first understand the volume formula for a cylinder, which is V = πr²h. The radius is half of the diameter, so for this tube, the radius (r) is 4 centimeters (8 cm diameter / 2). The height (h) of the cylinder is given as 20 centimeters.
Now, we can plug in these values to find the volume:
V = π × (4 cm)² × 20 cmV = π × 16 cm² × 20 cmV = π × 320 cm³V = 3.142 × 320 cm³V ≈ 1005 cm³ (rounded to the nearest whole number)Therefore, the approximate volume of the tube is 1005 cubic centimeters when rounded to the nearest whole cubic centimeter.
what is the approximate value of tan B?
Answers
For this case we have that by definition of trigonometric relations of rectangular triangles, that the tangent of an angle is given by the opposite leg to the angle on the leg adjacent to the angle. So:
[tex]tg (B) = \frac {16} {7}\\tg (B) = 2.2857[/tex]
Rounding the value we have 2.29
Answer:
Option D
ANSWER
D 2.29
EXPLANATION
The tangent ratio, is the ratio of the opposite side to the adjacent side.
The side adjacent to angle B is 7 units.
The side opposite to angle B is 16 units.
This implies that:
[tex] \tan(B) = \frac{16}{7} [/tex]
[tex]\tan(B) =2.29[/tex]
The correct answer is D.