Answer:
Option C
Kindly award branliest
Step-by-step explanation:
Tn = n(n + 1)
T1 = 1(1 +1) = 1(2) = 2
T2 = 2(2+1) = 2(3) =6
T3 = 3(3 + 1) = 3(4) = 12
T4 = 4(4 + 1) = 4(5) = 20
... It obeys
Quick algebra 1 question for some points!
Only answer if you know the answer, quick shout-out to Subtomex0, tysm for the help!
[tex] \frac{y}{x} = \frac{4}{ - 3} = \frac{8}{ - 6} = \frac{12}{ - 9} \\ this \: relation \: holds \: so \: y \: varies \\ directly \: with \: x[/tex]
[tex] \frac{ 4}{3} m = \frac{8}{ - 6} \\ m = \frac{ \frac{ - 8}{6} }{ \frac{3}{ - 4} } = \frac{8 \times 4}{6 \times 3} = \frac{32}{18} = 2 \\ multipling \: by \: 2[/tex]
2)[tex] \frac{y}{x} = \frac{ - 40}{ - 0.5} = \frac{8}{2.5} = \frac{5}{4} \\ \frac{y}{x} = 80 = 3.2 = 1.25 \\ this \: is \: untrue \: so \: y \: is \: not \\ varying \: directly \: with \: x[/tex]
[tex]no \: constant \: of \: variation[/tex]
4)[tex] \frac{y}{x} = \frac{21}{3} = \frac{31.5}{4.5} = \frac{38.5}{5.5 \\ } \\ \frac{y}{x} = 7 = 7 = 7 \\ y \: varies \: directl y\: with \: x \\ consant \: of \: var = \frac{y}{x} = 7[/tex]5)[tex] \frac{y}{x} = \frac{30}{6} = \frac{35}{7} = \frac{96}{8} \\ \frac{y}{x} = 5 = 5 = 12 \\ y \: does \: not \: vary \: directly \: with \: x[/tex]
A circle has a central angle measuring startfraction 7 pi over 6 endfraction radians that intersects an arc of length 18 cm. what is the length of the radius of the circle? round your answer to the nearest tenth. use 3.14 for pi.
The radius of this circle is (B) 4.9 cm.
To find the radius of the circle:To solve this problem, we need to, first of all, convert the angle from radians to degrees.
data;
length of an arc = 18cmangle = 7/6π radsπ= 3.14[tex]\frac{7\pi }{6rads} =210^{0}[/tex]
Length of an Arc:
The formula for the length of an arc is given:
[tex]l_{arc} =[/tex] θ/360 × [tex]2\pi r[/tex]
Let's substitute the values and solve:
[tex]18=\frac{210}{360} *2\pi r\\18=3.663r\\r=\frac{18}{3.663} \\r=4.9cm[/tex]
From the calculations above, the radius of this circle is 4.9cm.
Therefore, the radius of this circle is (B) 4.9 cm.
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Complete question
A circle has a central angle measuring 7pi/6 radians that intersects an arc of length 18 cm. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3.14 for pi.
(A) 3.7 cm
(B) 4.9 cm
(C) 14.3 cm
(D) 15.4 cm
Find the surface.area of the composite.figure...
11 in.
3 in.
6 in.
3 in.
H
8 in.
SA =
3 in.
6 in.
11 in.
[?] in.2
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13. Define the domain of the following
For the given diagram, the domain of the graph will be within the range [-2, 8]. Hence the required domain are {-2, 0, 1, 2, 8}
Domain of a functionThe domain of a function are the independent variable of the function for which it exists,
For graphs, the domain exists on the x-axis of the curve or line on the xy plane.
For the given diagram, the domain of the graph will be within the range [-2, 8]. Hence the required domain are {-2, 0, 1, 2, 8}
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Pack of 100 index cards , 15 cmx 10 cm paper density 200 gsm what is the area of the cards on the table
a)15000 square cm or 1.5 square meter
b)32
c)80 GSM
d)0.405 gram
refer to the following images for solutions :
Index cards are used for a wide range of applications and environments: in the home to record and store recipes, shopping lists, contact information, and other organizational data; in business to record presentation notes, project research and notes, and contact information; in schools as flashcards or other visual.
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Suppose you start with a full tank of gas (17 gallons) in your truck. After driving 3 hours, you now have 3 gallons left. If x is the number of hours you have been driving, then y is the number of gallons left in the tank. At what rate is the gas left in the tank changing
Step-by-step explanation:
in 3 hours the truck used 17 - 3 = 14 gallons.
that means it used
14 gallons / 3 hours = 14/3 gallons / hour
and that means it is using
14/3 × x gallons in x hours
y = 17 - (14/3 × x)
the gas left in the tank is decreasing by 14/3 gallons per hour.
See picture to answer!
Using the law of cosines, it is found that the length of side AB is of AB = 13.
What is the law of cosines?The law of cosines states that we can find the angle C of a triangle as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
in which:
c is the length of the side opposite to angle C.a and b are the lengths of the other sides.For this problem, the parameters are:
C = 120, a = 8, b = 7.
Hence:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
[tex]c^2 = 8^2 + 7^2 - 2(8)(7)\cos{120^\circ}[/tex]
[tex]c^2 = 169[/tex]
[tex]c = \sqrt{169}[/tex]
c = 13.
Hence AB = 13.
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Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
Find the measure of arc CFD.
The measure of the Central Angle indicated is; 45°
How to find the central angle of a circle?
The central angle will be the angle subtended at the center by arc FE and arc CB.
Now, we see that angle ∠FOB = 135° and since we know that sum of angles on a straight line is 180°, then we can say that;
Central Angle = 180° - 135° = 45°
Angle subtended by Arc CD at the center is;
θ = 180 - (81 + 45)
θ = 54°
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Can someone help me with this question please !!
Answer:
20 ft by 14 ft
Step-by-step explanation:
See attached image.
To prove quadrilateral WXYZ is a parallelogram, Travis begins by proving △WZY ≅ △YXW by using the SAS congruency theorem.
Quadrilateral W X Y Z is shown. A diagonal is drawn from point W to point Y. Sides W Z and X Y are parallel and congruent.
Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.
WY ≅ WY by the reflexive property.
∠ZWY ≅ ∠XWY by the corresponding ∠s theorem.
WX ≅ ZY by definition of a parallelogram.
WZ ≅ XY by the given.
The reasons Travis can use to prove both triangles are congruent by the SAS congruency theorem are:
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.WY ≅ WY by the reflexive property.WZ ≅ XY by the given.What is the SAS Congruency Theorem?The SAS congruency theorem states that two triangles are congruent when they both have two pairs of corresponding congruent sides and a pair of corresponding congruent included angles.
Given the image below, we have the following proof with the statement and reasons in bracket:
WZ ≅ XY [given]
WY ≅ WY [reflexive property]
∠ZWY ≅ ∠XYW [by the alternate interior ∠s theorem]
△WZY ≅ △YXW [by the SAS congruency theorem]
Therefore, the reasons Travis can use are:
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.WY ≅ WY by the reflexive property.WZ ≅ XY by the given.Learn more about the SAS congruency theorem on:
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Answer:
A. ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem;
B. WY ≅ WY by the reflexive property; & E. WZ ≅ XY by the given.
Step-by-step explanation: Trust Me! Answer is correct on Edge.
Good Luck! :)
Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.
A. ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem B. WY ≅ WY by the reflexive property E. WZ ≅ XY by the given
3.
There was an earthquake in San Francisco April 18, 1906. More recently there was another earthquake in Columbia June 27, 2014. Earthquakes are measured using the associated amplitude on the Richter scale. Let a1 be the amplitude for the San Francisco earthquake and a2 be the amplitude for the Columbian earthquake.
San Francisco earthquake equations is below
Columbia earthquake below (view image)
a. Use the properties of logs to determine how many more times severe was the San Francisco earthquake? The severity is equal to the ratio below:
a1/a2
Using the properties of logarithms, it is found that the San Francisco earthquake was 24.71 times more severe than the Columbian earthquake.
How to find the ratios of the intensity of earthquakes?As given in the problem, the intensities of the earthquakes are given by logarithms of base 10. Then, supposing that the intensities are [tex]R_1, R_2, R_1 > R_2[/tex], the ratio of the intensities is given by:
[tex]R = 10^{\frac{R_1}{R_2}}[/tex]
For this problem, the intensities are:
[tex]R_1 = 7.8, R_2 = 5.6[/tex]
Hence the ratio is:
[tex]R = 10^{\frac{7.8}{5.6}} = 24.71[/tex]
The San Francisco earthquake was 24.71 times more severe than the Columbian earthquake.
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(4) A taxi service charges Rs.100 as an initial fee and Rs.50 for each kilometer travelled. Write an algebraic expression for the total amount that has to be paid for a journey of x meters.
Answer:
f(x) = 50x + 100
Explanation:
The term "Rs. 100" is constant. The term "Rs. 50" keeps changing per km.
Linear equation: y = mx + b, where 'm' is rate of change, 'b' is constant
Equation built:
f(x) = 50x + 100
This will determine the cost for journey of x meters.
Which lines can you conclude are parallel given that M<7 m<11=180 Justify your conclusion with a theorem. Line c is parallel to line d by the Converse of the Alternate Interior Angles Theorem. Line c is parallel to line d by the Converse of the Same-Side Interior Angles Theorem. Line a is parallel to line b by the Converse of the Alternate Interior Angles Theorem. Line a is parallel to line b by the Converse of the Same-Side Interior Angles Theorem. 23
Lines a and b are parallel based on the Converse of Same-Side Interior Angles Theorem,
What is the Converse Same-Side Interior Angles Theorem?The Converse of Same-Side Interior Angles Theorem states that, if the sum of two interior angles on same side of a transversal equals 180 degrees, then the lines they lie on are parallel to each other.
Since M<7 + m<11 = 180, lines a and b are parallel based on the Converse of Same-Side Interior Angles Theorem,
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There are 4 reb balls, 6 white balls, and 3 green balls in a bag. If one ball is drawn the bag at random, what is the probability that it is not white?
Answer:
7/13
Step-by-step explanation:
in all there are 13 balls and the number of balls that aren't white are 7
Answer:
7/13
Step-by-step explanation:
To find the probability that it is not white
P( not white) = number of balls that are not white / total balls
The balls that are not white are red and green = 4+3
= (4+3)/ ( 4+6+3)
= 7/13
Line A is perpendicular to Line B.
If the slope of Line A is
-1/7
what is the slope of Line B?
[?]
Answer:
7
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other. For example, if line A has a slope of 2, then line B, perpendicular to line A, will have a slope of -0.5.
The product of the square of a number x and 2 subtracted from 3 is y.
The algebraic expression for the given statement is: 2x² - 3 = y.
How to Write an Algebraic Expression?To wrote an algebraic expression is translate a statement using numbers, variables, and mathematical sign into a mathematical statement.
Square of x is: x²
Product of x² and 2 is: 2x²
Thus, we would have:
2x² - 3 = y
The algebraic expression is: 2x² - 3 = y.
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Help with these two problems and show work please !!
Answer:
1) [tex]x_1=-1-2\sqrt{2},\ x_2=-1+2\sqrt{2}[/tex]
2) [tex]x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]
Step-by-step explanation:
[tex]{\large \textsf{ Quadratic Formula: }}x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]
Given quadratic equations:
1. [tex]x^2+2x-7=0[/tex]
2. [tex]4x^2-3=x^2-5x-4[/tex]
1. x² + 2x - 7 = 0
[tex]\implies a=\textsf{1},b=\textsf{2},c=\textsf{-7}[/tex]
Step 1: Substitute the given values into the formula and simplify.
[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{2})\pm \sqrt{(\textsf{2})^2-4(\textsf{1})(\textsf{-7})}}{2(\textsf{1})}\\\implies x&=\dfrac{-2\pm \sqrt{4-4(-7)}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{4+28}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{32}}{2}\end{aligned}[/tex]
Step 2: Simplify the radicand (under the square root).
[tex]\begin{aligned}x&=\dfrac{-2\pm \sqrt{16\times2}}{2}\\x&=\dfrac{-2\pm 4\times\sqrt{2}}{2}\\x&=\dfrac{-2\pm 4\sqrt{2}}{2}\end{aligned}[/tex]
Step 3: Separate into two solutions and simplify them.
[tex]\implies x_1&=\dfrac{-2 - 4\sqrt{2}}{2},\ x_2&=\dfrac{-2 + 4\sqrt{2}}{2}[/tex]
[tex]\begin{aligned}\implies x_1&=\dfrac{-2}{2}+\dfrac{- 4\sqrt{2}}{2},\ x_2=\dfrac{-2 + 4\sqrt{2}}{2}\\\implies {x_1&=\boxed{-1-2\sqrt{2}},\ x_2=\boxed{-1+2\sqrt{2}} \end{aligned}[/tex]
----------------------------------------------------------------------------------------------------------------
2. 4x² - 3 = x² - 5x - 4
Step 1: Set the equation to zero (by moving the "x² - 5x - 4" to the left).
4x² - 3 - x² + 5x + 4 = 0 [ Combine like terms. ]
3x² + 5x + 4 = 0
[tex]\implies a=\textsf{3},b=\textsf{5},c=\textsf{1}[/tex]
Step 2: Substitute the given values into the formula and simplify.
[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{5})\pm \sqrt{(\textsf{5})^2-4(\textsf{3})(\textsf{1})}}{2(\textsf{3})}\\\implies x&=\dfrac{-5\pm \sqrt{25-12}}{6}\\\implies x&=\dfrac{-5\pm \sqrt{13}}{6}\end{aligned}[/tex]
Step 3: Separate into two solutions.
[tex]\implies x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]
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Christopher decides that another road to be named Saturn Avenue is needed that will go past
the cleaners and be perpendicular to Sunshine Avenue. Determine the slope of the equation
of the line that represents Saturn Avenue. [Show your work. Draw and label Saturn Avenue
on the coordinate plane. (Optional)
Slope of the equation of the line that represents Saturn Avenue: slope =
y = 4 is the equation of the line that represents Saturn Avenue given that Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive. This can be obtained by using the formula for finding the equation of the line.
Find the equation of the line:
Equation of a line can be determined using the formula,
y = mx + c
where m is the slope of the line and c is the y - intercept.
m = rise/run = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)
Here in this question draw the line passing through cleaners and perpendicular to Planet Drive.
The point where x = 0 is (0, 4)
This means that y - intercept is 4
By considering two points on the line we can find the slope of the equation,
Consider the points (8, 4) and (16, 4)
m = rise/run = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)
m = (4 - 4)/(16 - 8) = 0/8 = 0
So we got that,
y - intercept of the line = 4 slope of the line = 0Putting in the equation of line we get,
y = mx + c
⇒ y = (0)x + 4 ⇒ y = 4
Hence y = 4 is the equation of the line that represents Saturn Avenue given that Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive. Determine the equation of the line that represents Saturn Avenue. Show your work. Draw and label Saturn Avenue on the coordinate plane.
Write an equation of the line point(2,-1) and parallel passing through y=3x-5 write in slope-intercept form
Answer:
y = 3x - 7
Step-by-step explanation:
Since the lines are parallel, the slopes will be the same. In this case 3. Now we have to find the y-intercept. We will use the slope (3), the x (2) and y (-1) to help us do this. We get the x and the y from the ordered pair given(2,-1).
y = mx + b
-1 = 3(2) + b Plug in what you know
-1 = 6 + b Subtract 6 from both sides
-7 = b
Now we can write the equation
y = 3x -7
Last year, during an investigation of the time spent reading e-mails on a daily basis, researchers found that on Monday the average time was 50 minutes. Office workers claim that with the increased spam and junk mail, this time has now increased. To conduct a test, a sample of 25 employees is selected with the following results: sample mean
The sample mean value is 0.26.
According to the statement we have given that the
Monday the average time was 50 minutes and we have to find the sample mean.
So, the values become
H(not):μ≤50
H(a):μ>50
Right Tail
The significance level, of the given number of employees then
α=0.05
And The value of sample mean, is
Z=x - u/i*(n)^1/2
then the value becomes
Z = 5.6 - 5/1.2*(25)^1/2.
then after calculating
Z= 1.6/1.2*5
Z= 0.26 And
Here The value of sample mean is 0.26.
So, The sample mean value is 0.26.
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Transformation example
Answer:
Rotation, Reflection, Dilation.
Step-by-step explanation:
Find the surface area of the composite figure.
8 cm
6 cm
7 cm
8 cm
SA =
6 cm
[ ? ] cm²
9 cm
6 cm
If you'd like,
you can use a
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Enter
Answer:
The Answer Is 382...
Step-by-step explanation:
Which value is not part of the five-number summary for the following data set?
35, 23, 24, 30, 28, 23, 27, 33, 27, 34, 30, 30
A. 29
B. 23
C. 31.5
D. 24
Answer:
D. 24
Step-by-step explanation:
The 5-number summary of a data set includes ...
minimum1st quartilemedian (2nd quartile)3rd quartilemaximumSummary valuesWhen the data are written in increasing order, they are ...
23 23 24 27 27 28 30 30 30 33 34 35
The minimum is the first value on the list, 23.
The first quartile is the average of the two middle values in the lower half of the data set: (24+27)/2 = 25.5.
The median is the average of the two middle values: (28+30)/2 = 29.
The third quartile is the average of the two middle values in the upper half of the data set: (30+33)/2 = 31.5.
The maximum is the last value on the list: 35.
Answer choicesA. 29 is the median
B. 23 is the minimum
C. 31.5 is the 3rd quartile
D. 24 is not part of the 5-number summary
Choose the equation that satisfies the data in the table.
Answer:
Step-by-step explanation:
the answer is D
the value of dimes in a vending machine is $1.70 more than what it contains in quarters.if there are 199 coins in all how many dimes and quarters are there
Using a system of equations, it is found that there are 147 dimes and 52 quarters in the machine.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of dimes.Variable y: Number of quarters.There are 199 coins, hence:
x + y = 199 -> y = 199 - x.
The value of dimes(each is worth $0.1) is $1.7 more than the sum of the quarters(each is worth $0.25), hence:
0.1x - 0.25y = 1.7.
Since y = 199 - x:
0.1x - 0.25(199 - x) = 1.7.
0.35x = 51.45
x = 51.45/0.35
x = 147
y = 199 - 147 = 52
There are 147 dimes and 52 quarters in the machine.
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can someone solve this for me ?
Answer: 113.1 ft^3
Step-by-step explanation:
We know the radius is 3 so substitute it in the formula like this...
V = 4/3 π (3)^3
Solve for (3)^3 which is 27.
Next multiply 4/3 by π. Which equals 4.1887....
Then multiply that answer by 27.
And your answer is 113.1 ft^3.
Answer:
[tex]V=108ft^{3}[/tex]
Step-by-step explanation:
[tex]V=\frac{4}{3}(3)(3)^{3}[/tex]
[tex]V=\frac{4}{3}(3)(27)[/tex]
[tex]V=\frac{4}{3} (81)=\frac{324}{3}[/tex]
[tex]V=108[/tex]
Hope this helps
A recipe for fruit punch calls for 333 liters of orange juice and 222 liters of pineapple juice. Jo creates a drink by mixing 444 liters of orange juice with 333 liters of pineapple juice. Which recipe will have the stronger pineapple taste
The jo's drink have stronger pineapple taste.
Given that fruit punch calls for 333 liters of orange juice and 222 liters of pineapple juice and Jo creates a drink by mixing 444 liters of orange juice with 333 liters of pineapple juice.
In the Recipe for fruit punch calls
The Number of liters of orange juice = 333.
The Number of liters of pineapple juice = 222.
Thus, Total number of liters of juice = 222+333= 555 liters
Now, % of pineapple juice in fruit punch is
P₁=(222/555)×100
P₁=0.4×100
P₁=40%
Further, % of orange juice in fruit punch is
O₁=(333/555)×100
O₁=0.6×100
O₁=60%
In Jo's drink
The Number of liters of orange juice = 444.
The Number of liters of pineapple juice = 333.
Thus, Total number of liters of juice = 444+333= 777 liters
Now, % of pineapple juice in jo's drink is
P₂=(333/777)×100
P₂=0.43×100
P₂=43%
Further, % of orange juice in jo's drink is
O₂=(444/777)×100
O₂=0.57×100
O₂=57%
Hence, the taste of both drinks was not the same, jo's drink will have a stronger pineapple taste and jo's drink will have a lesser orange taste.
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Select the correct answer. A linear function on a coordinate plane passes through (minus 5, minus 3), (0, minus 4), and (5, minus 5) Which equation describes the line graphed above? A. y = − 4 x − 5 B. y = − 1 5 x − 4 C. y = − 5 x − 4 D. y = − 4 x − 1 5
The linear function on a coordinate plane passes through (-5, -3) and (0, -4) is y = -1/5x-4
Linear functionLinear function are functions that has a leading degree of 1. The equation of a linear function is expressed as y = mx + b
where
m is the slope
b is the intercept
Given the coordinates (-5, -3) and (0, -4)
Slope = -4+3/0+5
Slope = -1/5
The y-intercept of the line will be -4
Determine the equation
y = -1/5x-4
Hence the linear function on a coordinate plane passes through (-5, -3) and (0, -4) is y = -1/5x-4
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Determine the missing coordinate in the ordered pair (?,5) so that it will satisfy x+6y=18
Questions, are all in picture, please solve
The function represents a cosine graph with axis at y = - 1, period of 6, and amplitude of 2.5.
How to analyze sinusoidal functions
In this question we have a sinusoidal function, of which we are supposed to find the following variables based on given picture:
Equation of the axis - Horizontal that represents the mean of the bounds of the function.Period - Horizontal distance needed between two maxima or two minima.Amplitude - Mean of the difference of the bounds of the function.Type of sinusoidal function - The function represents either a sine or a cosine if and only if trigonometric function is continuous and bounded between - 1 and 1.Then, we have the following results:
Equation of the axis: y = - 1Period: 6Amplitude: 2.5The graph may be represented by a cosine with no angular phase and a sine with angular phase, based on the following trigonometric expression:To learn more on sinusoidal functions: https://brainly.com/question/12060967
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