We make use of the row percentage for comparisons
How to determine the percentage of comparison?From the question, we have:
Row ⇒ Independent variableColumn ⇒ Dependent variableThe data represented by the independent variable is always used to make comparison
Since this variable is on the rows, then the row percentage would be used for comparisons
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Which shows all the exact solutions of 2sec^2 (x)-tan^4 (x)=-1? Give your answer in radians.
a) pi/3 + kpi and 2pi/3 + kpi
b) pi/3 +2kpi and 5pi/3 +2kpi
c) pi/4 +2kpi, 3pi/4 + 2kpi, 5pi/4 +2kpi, and 7pi/4 +2kpi
d) pi/3 + kpi, 2pi/3 +kpi, 4pi/3 +kpi, and 5pi/3 +kpi
Answer:
a. 1/3pi+kpi and 2/3pi+kpi
Step-by-step explanation:
2Sec²x
=2+2tan²x-(tan²x)²=-1
Let tan²x=u
-u²+2u+2=-1
-u²+2u+3=0
u²-2u-3=0
(u+1)(u-3)=0
u=-1,u=3
(tan x)²=-1(No solution)
(tan x)²=3
>>tan x=±sqrt(3)
I) tan x=sqrt(3)
>>tan(pi/3)=sqrt 3
Tan(pi+A) =tanA
Tan(pi+pi/3)=tan(pi/3)
>>tan(4/3pi)=sqrt(3)
>>x=4/3pi and 1/3pi
General solution: 1/3pi+kpi
ii) tan x=-sqrt(3)
x=2/3pi(At 2nd quadrant)
x=5/3pi(at 4th quadrant)
General solution: 2/3pi+kpi
When the sum of a list of integers is divided by the mean of the integers, the result is x. What does x represent?
Answer:
it is the number of intigers in the list
Based on the concept of integer and the options available, x does represent the number of 2 integers in the list.
What is Integers?An integer is a mathematical term that is known as the number zero, a positive natural number, or a negative integer with a minus sign.
Generally, Integers the negative numbers are the additive inverses of the corresponding positive numbers.
In this case, it has been mathematically proven that when the sum of a list of integers is divided by the mean of the integers the result x represents the total number of integers in the list.
Hence, in this case, it is concluded that the correct answer is option H. The numbers if integers in the list.
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Can anyone explain how to do mathematical induction. The question is below. Brainliest awarded for the right answer. Thanks.
The sum of the triangular numbers is [tex]\frac{n(n+1)(n+2)}{6}[/tex]
According to the question, the series of triangular numbers is given as in the form of the number of dots constituting the equilateral triangles i.e.
1, 3, 6, 10, 15 . . . . .n
triangular number are the sequence and series of the numbers and each number represents and constitute in visualization of series of equilateral triangle.
given series in the figure
1, 3, 6, 10, 15, . . . . . . ., n
each number represents the number of dots containing in triangle
now the series can be given by
[tex]S = \frac{n(n+1)}{2}[/tex] for n = 1, 2, 3, 4,. . . . .n
now , according to the question the sum of the series can be given as
⇒ ∑S
⇒ ∑[tex]\frac{n^2+n}{2}[/tex]
⇒ [tex]\frac{1}{2}[\sum n^2+\sum n]\\\frac{1}{2}[\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}] \\\frac{n(n+1)}{4}[\frac{(2n+1)}{3}+1] \\\frac{n(n+1)}{4}[\frac{(2n+1+3)}{3}] \\\frac{n(n+1)}{4}[\frac{(2n+4)}{3}] \\\frac{n(n+1)}{4}2[\frac{(n+2)}{3}]\\\frac{n(n+1)(n+2)}{6}[/tex]
Thus, the sum of the triangular number is given by [tex]\frac{n(n+1)(n+2)}{6}[/tex]
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A cake decorator is rolling a square of fondant into a rectangle. the area of the rectangle can be represented by the expression 1.5s(2s). simplify the expression representing the area. 3.5s 3s2 3.5s2 3s
Answer:3.5s2
Step-by-step explanation:
because I said so
Answer:
3.5s2
Step-by-step explanation:
because that guy said so and it was right
Solve the equation.
8-2x = -8x + 14
O x=-1
3
0x = - 1²/20
5
0x = ²/3
O x = 1
Answer:
D. x=1
Step-by-step explanation:
8-2x = -8x + 14
First, add 8x to both sides.
8+6x=14
Next, subtract 8 from both sides.
6x=6
Lasty, divide 6 from both sides.
x=1
Hope this helps!
If not, I am sorry.
PLEASE HELP FAST!!! A ladder leans against a building. The top of the ladder reaches a point on the building, which is 18 feet above the ground. The foot of the ladder is 7 feet from the building. Find the measure of the angle of elevation from the ground to the top of the ladder.
The measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees
Angle of elevation and depressionThese method is used to determine the side and angles of a triangle
From the question given, we have the following parameters
Base of the building = 7feet (Adjacent side)
Height of the building = 18 feet (Opposite side)
Required
angle of elevation of the building
Using the SineOppositeHypotenuse CosineAdjacentHypotenuse TangentOppositeAdjacent identity
tanФ = opp/adj
tanФ = 18/7
Ф = 68.73 degrees
Hence the measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees
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which choice is equivalent to the expression below? square root of -64
Step-by-step explanation:
[tex] \sqrt{ - 64 } = - 8[/tex]
so the answer you got pls mark branlist
please help me guys its math
What are the x- and y-coordinates of point c, which partitions the directed line segment from a to b into the ratio 5:8? round to the nearest tenth, if necessary. x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (–2.2, –6.3) (–2.4, –6.4) (2.7, –0.7) (1.2, –4.7)
The value of (x,y) is (1.2 , -4.7) , Option D is the right answer.
The complete question is
On a coordinate plane, a line is drawn from point a to point b. point a is at (7, negative 2) and point b is at (negative 8, negative 9). what are the x- and y-coordinates of point c, which partitions the directed line segment from a to b into the ratio 5:8? round to the nearest tenth, if necessary. x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (–2.2, –6.3) (–2.4, –6.4) (2.7, –0.7) (1.2, –4.7)
What are Coordinates ?Coordinates are the location of a point in an (x,y) plot.
The given data is
Coordinates of
A = (7,-2)
B = (-8,-9)
m:n = 5:8
The coordinates of partition has to be determined
The formula used is
[tex]\rm (x,y) = \dfrac{1}{m+n} *(nx_1 + mx_2 , ny_1+ny_2)\\\\\\\rm (x,y) = \dfrac{1}{5+8} *(5*-8 + 8*7 , 5*-9+8*-2)[/tex]
(x,y ) = (1.2 , -4.7)
Therefore Option D is the correct answer.
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A large apartment complex has 1,500 units, which are filling up at a rate of 10% per month. If the apartment complex starts with 15 occupied units, how many months will pass before the complex has 800 occupied units? (Assume logistic growth). Round to the nearest tenth.
The number of months before the complex would have 800 occupied units is 40 months.
How many months before the complex has 800 occupied units?The formula that can be used to determine the required value is:
(In FV / PV) / r
Where:
FV = 800 PV = present occupancy rate = 15 r = rate of filling up = 10%(In 800 / 15) / 0.1 = 40 months
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Answer: 47.3 months
Step-by-step explanation:
Please help! I'm not quite understanding this.
Answer:
d.) 21
Explanation:
Rules:
-|a| = -a|-a| = ax = |a| then x = ±aSolve:
[tex]\rightarrow \sf \dfrac{4|a|}{2} + |a-3|[/tex]
[insert a = -6]
[tex]\sf\rightarrow \dfrac{4|-6|}{2} + |-6-3|[/tex]
[simplify the following]
[tex]\sf\rightarrow \dfrac{4(6)}{2} + 9[/tex]
[tex]\sf\rightarrow 12 + 9[/tex]
[tex]\sf\rightarrow 21[/tex]
multiple answer problem
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: E.\:\: \overline{DC}[/tex]
or
[tex]\qquad \tt \rightarrow \: F.\:\:\overline{CD}[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
A line with two dots at ends (two ends) represents a line segment.
And it can be represented as :
[tex]\qquad \tt \rightarrow \: \overline{DC}[/tex]
or
[tex]\qquad \tt \rightarrow \: \overline{CD}[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
An ice cube is freezing in such a way that the side length s, in inches, is s(t)=1/2t+4, where it is in hours. The surface area of the ice cube is the function A(s) = 6s²_
Part A: Write an equation that gives the volume at t hours after freezing begins. (2 points)
Part B: Find the surface area as a function of time, using composition, and determine its range. (4 points)
Part C: After how many hours will the surface area equal 294 square inches? Show all necessary calculations. (4 points)
Help Please!!
The equation of volume will be V = [(1/2)t + 4]³. The surface area as a function of time will be A(s) = 3/2 t² + 24t + 96. The number of hours when the surface area equal 294 square inches will be 3 1/2 hours.
What is a function?Functions are found all across mathematics and are required for the creation of complex relationships.
Part A: The equation that gives the volume at t hours after freezing begins will be
V = s³
V = [(1/2)t + 4]³
Part B: The surface area as a function of time, using composition, and determine its range will be
A(s) = 6(1/2 t + 4)²
A(s) = 6 (t²/4 + 4t + 16)
A(s) = 3/2 t² + 24t + 96
Part C: The number of hours when the surface area equal 294 square inches will be
294 = 6(1/2 t + 4)²
49 = (1/2 t + 4)²
7 = 1/2 t + 4
1/2 t = 3
t = 3 1/2 hours
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Equation of a graph problem
Answer:
this quantity refers to the amount that a container can hold.
For which temperature will the model most accurately predict the time spent cooling? 0 100 300 400
The temperature that accurately describes the time that would have spent cooling is 300.
How to solve for the cooling time.We have the function as f(t) = 349.2(0.98)t
We have to solve for all of the values in the option
When t = 0
This would give us an infinite value for t hence it is not the answer.
When t = 100
we have 61.6
When t = 300
we have f(t) = 7.5
WHen t = 400
f(t) = -6.7
From the solved values the accurate one that has to talk about the time spent cooling is 300 at 7.5
Complete questionThe function f(t) = 349.2(0.98)t models the relationship between t, the time an oven spends cooling and the temperature of the oven. For which temperature will the model most accurately predict the time spent cooling? 0 100 300 400
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ab (2a²b² - 4b) = what is the answer
Answer:
2ab(a2b−2)
Step-by-step explanation:
how to graph y = 2|x + 3| - 4
The x-intercepts and the y-intercepts of the function is that determines the graph is:
x-intercepts = (-5,0) and (-1,0)y-intercepts = (0,2)How do we graph the function y = f(x) of an absolute equation?The function of an absolute equation can be graphed by determining the values of x-intercepts and the y-intercepts of the function.
From the given equation:
y = 2|x+3| - 4
To determine the y-intercepts, we need to set the values of x to zero, and vice versa for x-intercepts.
By doing so, the x-intercepts and the y-intercepts of the function is:
x-intercepts = (-5,0) and (-1,0)y-intercepts = (0,2)Therefore, since we know the x and y-intercepts, the graph of the absolute value can be seen as plotted below.
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To hire a bicycle it costs $6 for each day plus a fixed charge of $15
a) Maria pays $39 to hire a bicycle. How many days does she hire it for.
Answer:
4 days
Step-by-step explanation:
1) Derive a formula.
Let b = bicycle
Let x = the number of days
A set up equation: b = 6x + 15
2) If she pays 39 to hire a bicycle, substitute 39 into b, then solve for x.
39 = 6x + 15
39 - 15 = 6x
24 = 6x
24/6 = x
4 = x
x = 4
Since x is the number of days, she hired the bicycle for 4 days.
If x + y = 2 and x - y = 6, solve for x and y.
Answer:
Step-by-step explanation:
Givens
x + y = 2
x - y = 6
Solution
Just add the two equations together. The y's will drop out.
x + y = 2
x - y = 6 Add
2x = 8 Divide by 2
2x/2 = 8/2 Combine
x = 4 Substitute x = 4 into the top equation
x + y = 2
4 + y = 2 Subtract 4 from both sides
4-4+y=2-4 Combine
y = - 2
Answer
x = 4
y = -2
Find the measure of angle DCF=
help me please :)) ty
Answer:
∠ DCF = 39°
Step-by-step explanation:
the secant- secant angle DCF is half the difference of the measures of the intercepted arcs, that is
∠ DCF = [tex]\frac{1}{2}[/tex] (EG - DF) = [tex]\frac{1}{2}[/tex] (127 - 49)° = [tex]\frac{1}{2}[/tex] × 78° = 39°
Simply the function f(x)=7(3Square root 54^x)
Answer:
54 = 2 × 3 × 3 × 3 = 2 × 3³
[tex] f(x) = 7(\sqrt[3]{54})^x [/tex]
[tex] f(x) = 7(\sqrt[3]{3^3 \times 2})^x [/tex]
[tex] f(x) = 7(3\sqrt[3]{2})^x [/tex]
Initial value: x = 0
[tex] f(0) = 7(3\sqrt[3]{2})^0 [/tex]
[tex] f(0) = 7(1) [/tex]
[tex] f(0) = 7 [/tex]
The initial value is 7.
The domain is all real numbers.
The range is all real numbers greater than zero.
When f(a) = 227 + 32 - 3, evaluate f( - 1)
helpp
Step-by-step explanation:
[tex]f(x) = 2 {x}^{2} + 3x - 3[/tex]
[tex]f( - 1) = 2. {( - 1)}^{2} + 3.( - 1) - 3[/tex]
[tex]f( - 1) = 2 - 3 - 3[/tex]
[tex]f( - 1) = - 4[/tex]
Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
I'm pretty sure it is d... .......
Calculate -0.4 as a percentage of 1.8
Answer:
-22.2222222222%
Step-by-step explanation:
-0.4/1.8×100
A boat travels 333 km in 7 hours with a constant speed how far can it travel in 6 hours with the same speed
Answer:
258 km
Step-by-step explanation:
We can calculate the speed of the boat with (333km/7 hours) = 47.57 km/hr.
Assuming the same speed, the boat would travel (47.57 km/hr)*(6 hr) = 258 km
19.
(05.06 MC)
The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years. Which of the following is an appropriate line of best fit? (1 point)
Considering the given scatter-plot, the line of best-fit is given by:
y = 0.77857t + 3.7.
How to find the equation of the line of best-fit using a calculator?To find the equation, we need to insert the points (t,y) in the calculator.
In this problem, considering the scatter-plot, we have that:
The values of t are: 1, 2, 3, 4, 5, 6, 7.The values of y are: 3.8, 5.8, 6.2, 7.5, 7, 8.2, 9.2.Hence, using the calculator, the equation is:
y = 0.77857t + 3.7.
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Please help!!!! ASAP!!!!!!!!!!
Answer:
[tex]\sqrt[]{4+\frac{1}{25}y }[/tex]
Step-by-step explanation:
Transform - y-25^2=-100
divide
simplify
x plus-minus [tex]\sqrt[]{4+\frac{1}{25}y }[/tex]
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Which is the correct representation of the inequality?
Here we have.
-3(2x - 5) < 5*(2 - x)
First, we need to isolate x in one side, let's expand both sides:
-6x + 15 < 10 - 5x
15 - 10 < 6x - 5x
5 < x
This will be represented with a number line where we have an open circle at 5, and an arrow that goes to the right. So the correct option is:
"A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right."
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Helena sees this recipe for pastry. she says that the ratio of margarine to flour is 4:1 is Helena correct? explain your answer
pastry:200g flour pinch salt
50g margarine water to mix
50g lard
Answer:
NOsince it talks about a ratio of margarine to flour, we should write it in this form:
MARGARINE : FLOURSince we have a 50g margarine and a 200g flour, therefore, we write it as
➡️ 50 : 200 ➡️ 1 : 4
FINAL ANSWER SHOULD BE:
1 : 4Step-by-step explanation:
Ratio of MARGARINE TO FLOUR
Given that margarine is 50g and flour is 200g. Therefore,
Margarine:Flour ➡️ 50:200 = 1:4
To check:
A:B= C:D ➡️ 50:200= 1:4
▶️AD= BC ➡️ (50) (4) = (200) (1)
➡️ 200 = 200
☑️
Hope it helps
12 identically sized pieces of timber are
x
cm long when put together. How long is each individual piece?
Answer:
[tex]\frac{x}{12}[/tex] (x/12)
Step-by-step explanation:
if 12 pieces combine to make x, [we know they are identical], each piece must be 1/12 of x [1/12·x = x/12]
(think of it like this: "x" length must be divided amongst 12 pieces, so, we divide x/ 12)
Answer:
Timber=x/12
Step-by-step explanation:
12 pieces long is x, if the length of each one is same, so the length of each one is x/12.
