Answer: The area of triangle ΔXYZ is 12 square inches.
Step-by-step explanation:
Since we have given that
RS = 3 inches
XY = 2 inches
Area of ΔRST = 27 in²
Since ΔRST is similar to ΔXYZ.
So, using the "Area similarity theorem":
[tex]\dfrac{\Delta RST}{\Delta XYZ}=\dfrac{RS^2}{XY^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{3^2}{2^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{9}{4}\\\\\Delta XYZ=3\times 4=12\ in^2[/tex]
Hence, the area of triangle ΔXYZ is 12 square inches.
The area of triangle XYZ is found by squaring the ratio of the corresponding sides of the similar triangles and multiplying it by the area of the larger triangle RST. With the side length ratio of 2:3, the area ratio is (2/3)², resulting in an area of 12 in² for triangle XYZ.
The student's question involves determining the area of a smaller similar triangle (XYZ) given the area of the larger similar triangle (RST) and the lengths of corresponding sides. To solve, we utilize the property that similar triangles' areas are proportional to the square of the ratio of their corresponding sides.
Given:
Length of RS in triangle RST = 3 inches
Length of XY in triangle XYZ = 2 inches
Area of triangle RST (A1) = 27 in²
We establish the ratio of their sides as 2 inches (XY) / 3 inches (RS), which simplifies to 2/3. The ratio of their areas would then be (2/3)² because the area of similar triangles scales with the square of the ratio of their corresponding linear dimensions. Hence, the Area of triangle XYZ (A2) will be A1 × (2/3)².
A2 = 27 in² × (2/3)2 = 27 × 4/9 = 12 in².
The area of triangle XYZ is 12 in².
It cost $525 for 7adult tickets and 12 youth tickets to the hockey game. If the difference in price between adult ticket Nd youth ticket is $18, find the cost of a youth ticket
Final answer:
To find the cost of a youth ticket, you can set up a system of equations using the given information. Solve the system of equations to find the cost of a youth ticket.
Explanation:
To find the cost of a youth ticket, we can set up a system of equations using the given information. Let x be the cost of an adult ticket and y be the cost of a youth ticket. From the problem, we know that 7x + 12y = 525 and x - y = 18. We can solve this system of equations using substitution or elimination.
First, let's solve for x in terms of y using the second equation. Adding y to both sides gives x = y + 18.
Next, substitute this expression for x in the first equation: 7(y + 18) + 12y = 525. Simplifying this equation gives 7y + 126 + 12y = 525. Combining like terms, we get 19y + 126 = 525. Subtract 126 from both sides: 19y = 399. Finally, divide both sides by 19 to solve for y: y = 21.
Therefore, the cost of a youth ticket is $21.
Consider a circle whose size can vary. The circumference of the circle is always 2π times as large as its radius. Let r represent the radius of the circle (in feet) and let C represent the circumference of the circle (in feet).
a. Write a formula that expresses C in terms of r.
b. Use your formula from part (a) to determine the circumference of a circle whose radius is 6 feet feet
c. Write a formula that expresses r in terms of C.
d. Use your formula from part (c) to determine the radius of a circle whose circumference is 37
Answer:a) C = 2πr
b) 37.68feet
c) r = C/2π
d) 5.89feet
Step-by-step explanation:
The answers are a) 2πr, b) 37.68 ft, c) r = C/2π and d) 5.8 ft
What is circumference?The circumference is the distance around the edge of a circle.
Given that, a circle whose size can vary. The circumference of the circle is always 2π times as large as its radius and r represent the radius of the circle (in feet) and let C represent the circumference of the circle (in feet).
a) C = 2πr
b) C = 2*3.14*6 = 37.68ft
c) C = 2πr, r = C/2π
d) r = 37/2*3.14 = 5.8 ft
Hence, The answers are a) 2πr, b) 37.68 ft, c) r = C/2π and d) 5.8 ft
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A guy wire is used to support flagpoles in windy areas. These wires are anchored in the ground to provide constant stability. You need to replace the guy wire on a pole that is 20 feet tall.. The anchor point for this flagpole is 15 feet away from the base of the pole. a. How long is the wire you need to purchase to replace the old wire? b. You are also helping a friend determine the length of a guy wire for a 10-foot flagpole. The wire needs to be anchored 6 feet from the base of the pole. You can purchase guy wires in whole foot lengths only. Using your knowledge of perfect squares, estimate the length of wire you would need to complete the project. How much wire would be left over?
Answer: a) Length of wire to replace old one=9ft
b) Length of wire=3.09ft
Leftover wire=0.91ft
Step-by-step explanation: from the right angle triangle, Tan&=20/15
&=53.13°
Length of wire,x=cos 31.13=x/15
15cos31.13
X=9
b) Tan&=10/6
Tan^-110/6
&=59.05
Length= 6cos59.04
X=3.09
4-3.09=.91= leftover wire
Using the Pythagorean theorem, the length of the guy wire needed for a 20-foot flagpole with a 15-foot distant anchor point is 25 feet, and for a 10-foot flagpole with a 6-foot distant anchor point, a 12-foot guy wire is needed, leaving approximately 4 inches of wire leftover.
The question involves applying the Pythagorean theorem to determine the lengths of guy wires needed to support flagpoles. For the first scenario, a 20-foot tall flagpole with a 15-foot distant anchor point, the guy wire's length can be found using the equation a^2 + b^2 = c^2, where 'c' is the hypotenuse (the guy wire), 'a' is one leg (the height of the flagpole which is 20 feet), and 'b' is the other leg (the distance from the base of the pole to the anchor point which is 15 feet). After calculation, the guy wire's length is found to be 25 feet.
For the second scenario with a 10-foot tall flagpole and a 6-foot distant anchor point, using the same theorem gives us the equation 10^2 + 6^2 = c^2. Estimating using perfect squares, we get c as the square root of 136, which is approximately 11.66 feet. Since guy wires can only be purchased in whole foot lengths, we would purchase a 12-foot guy wire, leaving approximately 0.34 feet (about 4 inches) of wire leftover.
Points X and Z are on a number line, and point Y partitions XZ into two parts so that the ratio of the length of XY to the length of YZ is 5:7. The coordinate of X is 1.3, and the coordinate of Y is 3.8. What is the coordinate of Z?
Answer:
The coordinate of [tex]Z=7.3[/tex].
Step-by-step explanation:
To determine:
What is the coordinate of Z?
Fetching Information and Solution Steps:
Points X and Y are on a number linepoint Y partitions [tex]XZ[/tex] into two parts so that the ratio of the length of XY to the length of [tex]YZ[/tex] is 5:7The coordinate of X is 1.3the coordinate of Y is 3.8The distance [tex]XY[/tex] = [tex]3.8-1.3 = 2.5[/tex]
As
Y is [tex]\frac{5}{12}[/tex] of the way from [tex]X[/tex] to [tex]Z[/tex]
So,
[tex]YZ[/tex] is [tex]\frac{7}{5}[/tex] as big as [tex]XY[/tex]
Therefore,
[tex]Z = 3.8 + (\frac{7}{5} )(2.5)[/tex]
[tex]Z=3.8+\frac{17.5}{5}[/tex]
[tex]Z=7.3[/tex]
Therefore, the coordinate of [tex]Z=7.3[/tex].
Keywords: coordinate, point, length, ratio
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The coordinate of Z is (4.43, 11.57)
The coordinate of X is (1, 3)
The coordinate of Y is (3, 8)
Let the coordinate of z be (x₂, y₂)
The ratio of division is 5:7
m = 5, and n = 7
Let the coordinate of y be (a, b)
a = 3, b = 8
[tex]a=\frac{mx_1+nx_2}{m+n}\\\\3= \frac{5(1)+7x_2}{5+7}\\\\3(12)=5+7x_2\\\\7x_2=36-5\\\\7x_2=31\\\\x_2=4.43[/tex]
[tex]ab=\frac{my_1+ny_2}{m+n}\\\\8= \frac{5(3)+7y_2}{5+7}\\\\8(12)=15+7y_2\\\\7y_2=96-15\\\\7y_2=81\\\\y_2=11.57[/tex]
The coordinate of Z is (4.43, 11.57)
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Needing help here don’t have a clue
Answer:
v(9)=2000
V(15)=8000
Step-by-step explanation:
Answer:
Step-by-step explanation:
You are given a function V(t) and asked to find V(9) and V(15). In each case, the number in parentheses replaces "t" in the function expression. After that, it is just arithmetic. (You may want to use a calculator, but it isn't really necessary.)
Given:
V(t) = 250·2^(t/3)
Find:
V(9) = 250·2^(9/3)
= 250·2^3
= 250·8
V(9) = 2000
__
V(15) = 250·2^(15/3)
= 250·2^5
= 250·32
V(15) = 8000
_____
As you know, an exponent signifies repeated multiplication. The exponent tells you the number of times the base is a factor in the product:
2^3 = 2·2·2 = 8 . . . . . . the exponent of 3 means 2 is a factor 3 times
What is the horizontal asymptote of f (x) =StartFraction negative 2 x Over x + 1 EndFraction? y = –2 y = –1 y = 0 y = 1
Answer:
y = -2
Step-by-step explanation:
Any asymptotes of a rational function will be described by the quotient of the numerator and denominator (excluding any remainder).
[tex]f(x)=\dfrac{-2x}{x+1}=-2+\dfrac{2}{x+1}[/tex]
The horizontal asymptote is ...
y = -2
Answer:
y = –2Step-by-step explanation:
The given function is
[tex]f(x)=\frac{-2x}{x+1}[/tex]
An asymptote refers to a restriction in the domain or range set of the function. This happens to rational functions, because there's a scenario where the function is undetermined: when its denominator is zero.
So, in this case, the value that makes the denominator zero is
[tex]x+1=0\\x=-1[/tex]
That means, we need to restrict the domain for [tex]x=-1[/tex]. But this is a vertical asymptote.
To find horizontal asymptotes, we need to find the restrictions for the range of the function, we do that isolating [tex]y[/tex].
[tex]y=\frac{-2x}{x+1}\\yx+y=-2x\\yx+2x=-y\\x(y+2)=-y\\x=-\frac{y}{y+2}[/tex]
So, if we analyse the denominator
[tex]y+2=0\\y=-2[/tex]
Therefore, the restriction is [tex]y=-2[/tex]. In other words, the vertical asymptote is the first choice.
The sum of four numbers in arithmetic progression is 16. The square of the last number is the square of the first number plus 48. What are the four numbers?
Answer:
four numbers are 1, 3, 5, 7
Step-by-step explanation:
The sum of four numbers in arithmetic progression is 16
a, a+d, a+2d, a+3d are the four arithmetic series
sum of 4 numbers are
[tex]a+a+d+a+2d+a+3d=4a+6d[/tex]
[tex]4a+6d= 16[/tex]
divide both sides by 2
[tex]2a+3d=8[/tex]
[tex]3d= 8-2a[/tex]
The square of the last number is the square of the first number plus 48.
[tex](a+3d)^2=a^2+48[/tex]
solve for a and d
[tex](a+3d)^2=a^2+48\\(a+8-2a)^2=a^2+48\\(8-a)^2=a^2+48\\a^2-16a+64=a^2+48\\-16a=48-64\\-16a=-16\\a=1[/tex]
Now find out 'd'
[tex]3d=8-2a\\3d=8-2\\3d=6\\a=2[/tex]
a, a+d, a+2d, a+3d
four numbers are 1, 3, 5, 7
Which choice correctly expresses the solution set in the inequality in words?
Answer:
The answer to your question is letter A.
Step-by-step explanation:
Inequality x + 2 ≥ 5
Solve the inequality, remember that inequalities and equations are solved in similar ways.
- Subtract 2 in both sides
x +2 - 2 ≥ 5 - 2
- Simplify
x ≥ 3
- Remember that this sign "≥" means that x is greater or equal to a number, and this sign "≤" means that x is lower or equal to a number.
The option that satisfies our inequality is the first option.
Adnan made "x" calculators this week, but Maya made twice as many calculators. Write an algebraic expression for the number of calculators that Maya made this week. A) 2x B) x + 2 C) x 2 D) x − 2
Answer:
A) [tex]2x[/tex]
Step-by-step explanation:
Given:
Number of calculator made by Adnan in this week = [tex]'x'[/tex]
We need to write an algebraic expression for the number of calculators that Maya made this week.
Solution:
Now given:
Maya made twice as many calculators.
So we can say that;
Number of calculators made by Maya this week is equal to 2 times Number of calculator made by Adnan this week.
framing in equation form we get;
Number of calculators made by Maya this week = [tex]2\times x = 2x[/tex]
Hence an algebraic expression for the number of calculators that Maya made this week is [tex]2x[/tex].
A triangular prism is 19.1 meters long and has a triangular face with a base of 18 meters and a height of 12 meters. The other two sides of the triangle are each 15 meters. What is the surface area of the triangular prism?
Answer:
A= 1132.8 m^2
Step-by-step explanation:
l=19.1m
b=18m
h=12m
s=15m
The formula to find surface area of the triangular prism is:
A = bh + 2ls + lb
A = (18×12) + 2(19.1×15) + (19.1×18)
A = 216 + 573 + 343.8
A= 1132.8 m^2
Answer: surface Area of triangular prism = 502.5m^2
Step-by-step explanation:
Formular for surface area of a prism is given as: SA=bh+(S1 +S2+S3)H
Given base =18m, length=19.1, h=12, w=15
S1=1/2bh =1/2×18×12 =108m
S2=108m . This is because the dimensions of the two ends of the triangular prism.
S3=lw=19.1×15=286.5m
Surface area=108+108+286.5=502.5m^2
A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Calculate the chi-square test statistic x2 to determine if there is enough evidence to conclude that the number of minutes spent online per day is related to gender. Minutes spent online per day Gender 0-30 30-60 60-90 90+Male 75 45 25 35 Female 30 45 45 15 A) 19.874 B) 18.146 C) 20.912 D) 21.231
Answer:
There is enough evidence to conclude that the number of minutes spent online per day is related to gender
Step-by-step explanation:
Given that a researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below.
Gender 0-30 30-60 60-90 90+ total
Males 75 45 25 35 180
Females 30 45 45 15 135
H0: there is no association between gender and spending time online
Ha: There is association
(Two tailed test)
Expected for each cell is calculated as row total*grand total/column total
<30 30-60 60-90 >90 Row Totals
Males 75 (60.00) [3.75] 45 (51.43) [0.80] 25 (40.00) [5.62] 35 (28.57) [1.45] 180
Females 30 (45.00) [5.00] 45 (38.57) [1.07] 45 (30.00) [7.50] 15 (21.43) [1.93] 135
chi square -= 27.125
p value <0.0001
Since p is less than 1% (significance level) we reject the null hypothesis
There is enough evidence to conclude that the number of minutes spent online per day is related to gender
Answer:
The answer would be 18.146
Step-by-step explanation:
Given that a researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below.Gender 0-30 30-60 60-90 90+ totalMales 75 45 25 35 180Females 30 45 45 15 135H0: there is no association between gender and spending time onlineHa: There is association(Two tailed test)Expected for each cell is calculated as row total*grand total/column total<30 30-60 60-90 >90 Row TotalsMales 75 (60.00) [3.75] 45 (51.43) [0.80] 25 (40.00) [5.62] 35 (28.57) [1.45] 180Females 30 (45.00) [5.00] 45 (38.57) [1.07] 45 (30.00) [7.50] 15 (21.43) [1.93] 135chi square -= 27.125p value <0.0001Since p is less than 1% (significance level) we reject the null hypothesisThere is enough evidence to conclude that the number of minutes spent online per day is related to gender
Simplify the complex expression and show work
The answer is
[tex](-9+3\sqrt{2})+(3\sqrt{2}-2)i[/tex]
=======================================================
Work Shown:
[tex](-3+\sqrt{-2})(3-\sqrt{2})[/tex]
[tex](-3+\sqrt{-1*2})(3-\sqrt{2})[/tex]
[tex](-3+\sqrt{-1}*\sqrt{2})(3-\sqrt{2})[/tex]
[tex](-3+i\sqrt{2})(3-\sqrt{2})[/tex]
[tex]x(3-\sqrt{2})[/tex] let [tex]x=-3+i\sqrt{2}[/tex]
[tex]3x-x*\sqrt{2}[/tex] distribute
[tex]3(x)-\sqrt{2}(x)[/tex]
[tex]3(-3+i\sqrt{2})-\sqrt{2}(-3+i\sqrt{2})[/tex]
[tex]-9+3i\sqrt{2}+3\sqrt{2}-i*\sqrt{2}*\sqrt{2}[/tex]
[tex]-9+3i\sqrt{2}+3\sqrt{2}-2i[/tex]
[tex]-9+3\sqrt{2}+3i\sqrt{2}-2i[/tex]
[tex](-9+3\sqrt{2})+(3\sqrt{2}-2)i[/tex]
The use of parenthesis in the last step is to help separate out the terms.
The last expression shown above is in the form a+bi where
[tex]a=-9+3\sqrt{2}[/tex]
[tex]b=3\sqrt{2}-2[/tex]
Find the sum . 1 1/3+(-2 1/6 ) =? Please write out the steps
Answer:
-5/6
Step-by-step explanation:
covert the mixed number into a improper fraction
4/3 + (- 13/6) =
Find LCD which is 6 so
[tex]\frac{4}{3} * 2[/tex]
8/6 + (-13/6) =
Which is -5/6
A rectangular tank that is 5324 ft cubed with a square base and open top is to be constructed of sheet steel of a given thickness. Find the dimensions of the tank with minimum weight.
Answer:
Side of 22 and height of 11
Step-by-step explanation:
Let s be the side of the square base and h be the height of the tank. Since the tank volume is restricted to 5324 ft cubed we have the following equation:
[tex]V = s^2h = 5324[/tex]
[tex]h = 5324 / s^2[/tex]
As the thickness is already defined, we can minimize the weight by minimizing the surface area of the tank
Base area with open top [tex]s^2[/tex]
Side area 4sh
Total surface area [tex]A = s^2 + 4sh[/tex]
We can substitute [tex]h = 5324 / s^2[/tex]
[tex]A = s^2 + 4s\frac{5324}{s^2}[/tex]
[tex]A = s^2 + 21296/s[/tex]
To find the minimum of this function, we can take the first derivative, and set it to 0
[tex]A' = 2s - 21296/s^2 = 0[/tex]
[tex]2s = 21296/s^2[/tex]
[tex]s^3 = 10648[/tex]
[tex]s = \sqrt[3]{10648} = 22[/tex]
[tex]h = 5324 / s^2 = 5324 / 22^2 = 11[/tex]
To find the dimensions of the rectangular tank with a square base and minimum weight, we set up the volume and surface area formulas in terms of the base's side length and the tank's height, then use calculus to find the dimensions that minimize the surface area.
Explanation:The problem is a typical unconstrained optimization problem in calculus. The volume of the tank is given as 5324 cubic feet. Since it's a rectangular tank with a square base, we can let x be the length of the side of the base and h be the height of the tank. Then, the volume of the tank is x^2*h = 5324.
The weight of the tank is proportional to the amount of steel used, which, in turn, is proportional to the surface area of the tank. The surface area of the tank is x^2 + 4*x*h. From the volume formula, we can express h in terms of x: h = 5324 / x^2. Substituting it to the surface area formula, we get the surface area is a function of x, such that "A = x^2 + 4x * 5324 / x^2".
To find the dimensions that minimize the weight, we find the derivative of A with respect to x and set it equal to 0. This will give the x that minimizes the surface area. Then substitute this value back into the equation h = 5324 / x^2 to get the optimal height.
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Find an equation for those points P such that the distance from P to A(0, 1, 2) is equal to the distance from P to B(6, 4, 2). What is this set?
Answer: The required equation for points P is [tex]4x+2y=17.[/tex]
Step-by-step explanation: We are give two points A(0, 1, 2) and B(6, 4, 2).
To find the equation for points P such that the distance of P from both A and B are equal.
We know that the distance between two points R(a, b, c) and S(d, e, f) is given by
[tex]RS=\sqrt{(d-a)^2+(e-b)^2+(f-c)^2}.[/tex]
Let the point P be represented by (x, y, z).
According to the given information, we have
[tex]PA=PB\\\\\Rightarrow \sqrt{(x-0)^2+(y-1)^2+(z-2)^2}=\sqrt{(x-6)^2+(y-4)^2+(z-2)^2}\\\\\Rightarrow x^2+y^2-2y+1+z^2-4z+4=x^2-12x+36+y^2-8y+16+z^2-4z+4~~~~~~~[\textup{Squaring both sides}]\\\\\Rightarrow -2y+1=-12x-8y+52\\\\\Rightarrow 12x+6y=51\\\\\Rightarrow 4x+2y=17.[/tex]
Thus, the required equation for points P is [tex]4x+2y=17.[/tex]
WILL GIVE BRAINLIEST NEED HELP ASAP THANK YOU <3
Answer:
False
Step-by-step explanation: Are you asking whether or not its false? If so then yes f(x) is not a function because the x's on the left side repeat. Example the six points to two different numbers on the right side. I hope i helped!
Answer:
your answer is correct
Step-by-step explanation:
When a relation has an input that maps to more than one output, it is not a function. Both 6 and 12 map to two different outputs, so the relation is not a function. Your answer choice is correct.
Find the midpoint of (0,4) and (-4,-12)
A delivery truck has 40,000 miles on its odometer and travels an average of 22,000 miles per year.
Which function best models the linear relationship?
Answer:
y=22000x+40000
Please help asap i really need this. Brainliest. Using Square Roots to Solve Equations.
Answer:
The answer to your question is below
Step-by-step explanation:
a) x² = 196
x = ±√196
x = ± 14 or x = -14 and x = 14
b) 9x² = 49
x² = 49/ 9
x = √(49/9)
x = ±7/3
x = ± 2.3 or x = 2.3 and x = -2.3
c) 4x² - 8 = 56
4x² = 56 + 8
4x² = 64
x² = 64/4
x² = 16
x = ±√16
x = ±4 or x = 4 and x = -4
d) x² = 160
x = ± √160
Find the prime factors of 160
160 2
80 2
40 2
20 2
10 2
5 5
1 160 = 2⁵5
x = √2⁴10
x = ±4√10
e) x² = 72
Find the prime factor of 72
72 = 2²3²6
x = √2²3²6
x = ±6√6 or
x = ±8.5
John is building a custom wall for a kitchen remodel. He knows the space for the wall is square with an area of 121 feet. How long does his diagonal brace need to be?
Answer:
His diagonal brace need to be 15.55 feet long in the kitchen.
Step-by-step explanation:
Given : The wall of the kitchen is in the shape of a square.
Area of the wall = 121 sq ft
Let us assume the each side of wall = a ft
Now, AREA OF THE SQUARE = Side x Side
⇒ a x a = 121 sq units
[tex]\implies a ^2 = 121\\\implies a = 11[/tex]
So, each side of the kitchen wall is 11 ft.
Now,as we know in a square : EACH ANGLE IN THE SQUIRE IS A RIGHT ANGLE.
So, by Pythagoras Theorem, Diagonal D is:
[tex]D^2 = a^2 + a^2\\\implies D^2 = 11^2 + 11^2 = 121 + 121\\\implies D^2 = 242\\\implies D = 15.55[/tex]
Hence, his diagonal brace need to be 15.55 ft long in the kitchen.
A gardener is planting two types of trees: Type A is 5 feet tall and grows at a rate of 13 inches per year. Type B is 3 feet tall and grows at a rate of 21 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:it will take 0.25 years
Step-by-step explanation:
Let x represent the number of years that it will take for type A and tree B to be the same height.
Let y represent the height of type A after x years.
Let z represent the height of type B after x years.
Type A is 5 feet tall and grows at a rate of 13 inches per year. This means that
y = 5 + 13x
Type B is 3 feet tall and grows at a rate of 21 inches per year. This means that
z = 3 + 21x
To determine the number of years it will take both trees to be of the same height, we would equate equation y to z. It becomes
5 + 13x = 3 + 21x
21x - 13x = 5 - 3
8x = 2
x = 2/8 = 0.25 years
Name at least 2 major similarities between the sheep and human brains that you did not name in your hypothesis, but that you observed or learned about during the dissection.
Answer:
Step-by-step explanation: The brains are very similar insofar that they function in almost the same way when it comes to controlling physical aspects of our existence. Our brains regulate our organs and our body parts just like a sheep's brain.
Perform the requested operation or operations.
f(x) = 4x + 9, g(x) = 4x2
Find (f + g)(x).
16x3 + 36x
four x plus nine divided by four x squared.
4x + 9 - 4x2
4x + 9 + 4x2
Answer:
[tex]4x+9+4x^2[/tex]
Step-by-step explanation:
The given functions are:
[tex]f(x)=4x+9[/tex] and [tex]g(x)=4x^2[/tex]
We want to find [tex](f+g)(x)[/tex].
Recall that:
[tex](f+g)(x)=f(x)+g(x)[/tex]
We substitute the functions to get:
[tex](f+g)(x)=4x+9+4x^2[/tex]
We now write in standard form to obtain:
[tex](f+g)(x)=4x^2+4x+9[/tex]
PLEASE HELP!!!! (100 PTS)
Answer:
(x) free throw = 8
(y) 2-point = 6
(z) 3-point = 2
x+(y*2)+(z*3)
8+(6*2)+(2*3)
8+12+6
=26
The phenomenon that involves the misperception of the length of two identical lines, one with arrows pointing outward and one with arrows pointing inward is called the:
Müller-Lyer illusion. (T/F)
Answer:
True
Step-by-step explanation:
Müller-Lyer illusion - In this illusion two-line having the same length appear to be different from one another.
the line showing in the file attached, the line with arrow moving outward appears to have large length and line having the arrow pointing inward appear to have a short length. But given lines are equal in length, it is just an illusion that might force to believed you that one is shorter or larger than others.
Write an expression for the sequence of operations.
Subtract 4 from x, double, and add 8.
The expression for the given sequence of operations is 2(x-4)+8.
The given statement is "subtract 4 from x, double, and add 8".
We need to write an expression for the sequence of operations.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Now, subtract 4 from x=x-4
Double the difference that is 2(x-4)
Add 8=2(x-4)+8
Therefore, the expression for the given sequence of operations is 2(x-4)+8.
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An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is the probability that each of the balls will be (a) of the same color?
Answer:
As a fraction, the answer is exactly 86/969
In decimal form, the answer is approximately 0.08875
=====================================================
Work Shown:
The assumption is that no replacements are made for each selection.
5 red, 6 blue, 8 green
5+6+8 = 19 total
A = P(3 red) = (5/19)*(4/18)*(3/17) = 10/969
B = P(3 blue) = (6/19)*(5/18)*(4/17) = 20/969
C = P(3 green) = (8/19)*(7/18)*(6/17) = 56/969
D = P(3 all same color)
D = A+B+C
D = 10/969 + 20/969 + 56/969
D = (10+20+56)/969
D = 86/969
D = 0.08875
A particle that moves along a straight line has velocity v(t) = t 2 e −t meters per second after t seconds. How far will it travel during the first t seconds?
The distance traveled by the particle is determined as [tex]\int\limits^0_t {v(t)} \, dt=-e^{-t}t^{2}+2(-e^{-t}t-e^{-t})+2[/tex].
Given data:
To determine the distance traveled by the particle during the first t seconds, integrate the velocity function with respect to time over the interval [0, t].
Given the velocity function:
[tex]v(t) = t^2 * e^{(-t)}[/tex]
To find the distance traveled, integrate the absolute value of the velocity function over the interval [0, t]:
[tex]\text{distance} = \int\limits^0_t {v(t)} \, dt[/tex]
Since the velocity can be negative (indicating a change in direction), taking the absolute value ensures that we consider the magnitude of the velocity.
Now, calculate the integral:
[tex]D = \int\limits^0_t {t^2 * e^{(-t)}} \, dt[/tex]
To simplify this integral, split it into two parts, considering the cases when the velocity is positive and negative:
[tex]D=[-e^{-t}t^2-\int\limits^0_t {-2e^{-t}} \, dt]_0^t[/tex]
The first integral represents the distance traveled when the velocity is positive, and the second integral represents the distance traveled when the velocity is negative.
Integrating each term separately:
[tex]\int\limits^0_t {v(t)} \, dt=-e^{-t}t^{2}+2(-e^{-t}t-e^{-t})+2[/tex]
Hence, the distance is [tex]D=-e^{-t}t^{2}+2(-e^{-t}t-e^{-t})+2[/tex].
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The complete question is attached below:
A particle that moves along a straight line has velocity [tex]v(t) = t^2e^{-t}[/tex] meters per second after t seconds. How far will it travel during the first t seconds?
The function v(t) = t2 e−t defines the velocity of a particle. The displacement or distance covered by the particle in the first t seconds is given by the integral from 0 to t of the velocity function.
Explanation:
The given velocity function for the particle is v(t) = t2 e−t. The distance (or displacement) traveled by an object is the integral of the velocity over a given interval. So, to find the distance covered by the particle in the first t seconds, you would set up the following integral:
∫0t t2 e−t dt
We won't compute this integral here, as it requires knowledge of methods beyond basic calculus, specifically the use of integration by parts and possibly a tabular method for successive integrations by parts. However, this setup gives you the right starting point to find the distance covered in the first t seconds.
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Triplets Adam, Bruce, and Charlie enter a triathlon. If there are 9 competitors in the triathlon and medals are awarded for first, second, and third place, what is the probability that at least two of the triplets will win a medal?
Answer: Probability that at least two of the triplets will win a medal is19/24
Step-by-step explanation:
Total number of cmpetitors=9
Total number of selecting 3 winners out of 9 competitors=9C3=84
Number of ways of selecting 2 out of 3 triplets=3C2
Number of selecting 1 out of 6 others =6C1
Number of selecting 2 out of 3 triplet and o1 out of 6 others= 3C2 ×6C1=18
Number of selecting 3 out of 3 triplets=3C3=1
Total ways of selecting less than 2 or 2 triplets= 18+1=19
Probability that at least 2 of the triplets will win is 19/84
Using your calculator and rounding your answers to the nearest hundredth, find the remaining trigonometric ratios of θ based on the given information. sin θ = 0.26 and θ is in QI
Answer: 15.07°
Step-by-step explanation:
Sin^-1 0.26= 15.07°
Therefore:
Cos15.07= 0.9656
Tan 15.07 = 0.2692
Csc15.07= 1/(Sin15.07)= 3.846
Sec15.07=1/cos15.07=1.0356
Cot15.07=1/tan15.07= 3.7147
We can use the trigonometric identity sin² θ + cos² θ = 1 to find cos θ in a first quadrant triangle where sin θ = 0.26, and get cos θ = 0.966. Then, we calculate tan θ with the formula tan θ = sin θ / cos θ, and get tan θ = 0.269 after rounding.
Explanation:In trigonometry, there are three primary ratios called trigonometric ratios: sine (sin), cosine (cos), and tangent (tan). These ratios can be defined using the sides of a right triangle, and they relate the angles of a triangle to the lengths of its sides. If we know one of these ratios in a right triangle, we can find the others.
In this case, we know that sin θ = 0.26 and θ is in Quadrant I. In the first quadrant, all the trigonometric ratios are positive.
So, firstly we find cos θ. Remember that sin² θ + cos² θ = 1, we can solve for cos θ using the calculator with the square root of (1 - sin² θ), which results in cos θ = 0.966 approximately.
Next, to find tan θ, we use the relationship tan θ = sin θ / cos θ. So, tan θ = 0.26 / 0.966 = 0.269 approximately, after rounding to the nearest hundredth.
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