Given:
cos(2t) = 0.8
Take the cos⁻' of both-side of the equation.
cos⁻' cos(2t) = cos⁻'(0.8)
2t = cos⁻'(0.8)
Calculate the value of the right- hand side with your calculator in radians.
2t =0.6435
Divide both-side of the equation by 2
t ≈ 0.32
HELP PLS A line includes the points (9,10) and (6,9). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answer:
[tex]y-10=\dfrac{1}{3}(x-9)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
To find the equation of a line that passes through two given points, first find its slope by substituting the given points into the slope formula.
Define the points:
(x₁, y₁) = (9, 10)(x₂, y₂) = (6, 9)Substitute the points into the slope formula:
[tex]\implies m=\dfrac{9-10}{6-9}=\dfrac{-1}{-3}=\dfrac{1}{3}[/tex]
Therefore, the slope of the line is ¹/₃.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:
[tex]\implies y-10=\dfrac{1}{3}(x-9)[/tex]
Do the side measures 35 mm, 53 mm and 70 mm create a triangle?Yes, there are infinitely many triangles that can be created.No, it is impossible to create a triangle with the given measures.Yes, there is a unique triangle that can be created.Yes, there are two triangles that can be created.
Hello!
Let's call these sides a, b, and c:
• a = 35mm
,• b = 53mm
,• c = 70mm
To be a triangle, it must satisfy the existence condition of triangles, that is:
Let's check each of them:
[tex]\begin{gathered} |b-c|Answer:
Yes! There are infinitely many triangles that can be created.
What is the position of see on the number line belowWrite your answer as a fraction or mixed number
Answer:
1/3
Explanation:
We can see that from 0 to 1 the number line is divided into 6 parts and the point is right after the second part. Therefore, the fraction that represents point C is 2/6
This fraction is also equal to 1/3 because we can divide the line from 0 to 1 into 3 parts and take the first. The point will be at the exact same position of C.
Therefore, the answer is:
1/3
Which graph represents the table below?
Answer:
The answer will be D because you have to look very close and make sure the 1 is on the x-intercept and not the y-intercept.
6. A profit function for a new business follows the functionP(x) = 1/3x^2 - 6x, where x represents the number of months.After how many months will the company begin to make aprofit?A. 2B. 9C. 12D. 18
ANSWER
It will take 18 months before the company starts making a profit.
STEP-BY-STEP EXPLANATION
Given information
[tex]P(x)\text{ = }\frac{1}{3}x^2\text{ - 6x}[/tex]Where x is the number of months.
Step 1: Make P(x) = 0
[tex]\begin{gathered} \text{ p(x) = }\frac{1}{3}x^2\text{ - 6}x \\ 0\text{ = }\frac{1}{3}x^2\text{ - 6}x \end{gathered}[/tex]Step 2: Find x from the above equation
[tex]\begin{gathered} 0\text{ = }\frac{1}{3}x^2\text{ - 6x} \\ \text{Add 6x to the both sides} \\ 0\text{ + 6x = }\frac{1}{3}x^2\text{ - 6x + 6x} \\ 6x\text{ = }\frac{1}{3}x^2 \\ \text{cross multiply} \\ 6x\text{ }\times3=x^2 \\ 18x=x^2 \\ \text{Divide both sides by x} \\ \frac{18\cancel{x}}{\cancel{x}}\text{ = }\frac{\cancel{x^2}}{\cancel{x}} \\ x\text{ = 18 months} \end{gathered}[/tex]Therefore, it will take 18 months before the company starts making a profit.
Graph the line that has an x-intercept of (-1,0) and a y-intercept of (0,5). What is the slope of this line?
Answer:
The slope is 5.
Step-by-step explanation:
To solve this, you could have plotted the two points, drew a line between them, and then calculated the slope by counting on the graph the line's rise/run.
To slove this by finding the slope with the points:
(5 - 0) / (0 - - 1) = 5 / 1 = 5
The slope is 5
Columbia Mirror and Glass pays Janet Murphy a $1120 monthly salary plus a 14% commission on merchandise she sells each month. Assume Janet's sales were $94,100 for last month. Calculate the following amounts: 1. Amount of Commission: Х ? SUD si 2. Gross Pay:
Monthly salary = $1120
Comission percentage = 14%
Janet's sales = $94,100
1. Amount of commission
Multiply the sales amount (94,100) by the Commission percentage in decimal form (divided by 100).
94,100 x (14/100) =
94,100 x 0.14 = $13,174
2. Gross pay
Add the amount of commission and the monthly salary:
13,174+1120 = $14,294
I need help with this question Write and expression that models the situation:Sarah has spent x dollars out of the 30 dollars she started with.
Okay, here we have this:
Considering that it says "spent", it represents an outflow of money, therefore we take it as negative, so we obtain:
Actual Situation: Initial money - money spent
Actual Situation: 30 - x
Given ARPMAYC. complete each of the following statementsAYC9) AMPKAYAa) A d) 4YEb) CYe) EKc) PAZACYh) Al Aca
The triangles KMP and AYC, are congruent angles, because we are told that:
[tex]\text{KMP}\cong AYC[/tex]Thus, to find our answers we compare both triangles.
a) KM is approximately equal to AC.
That is because, as we can see in the following image, they are corresponding sides:
[tex]KM\cong AC[/tex]b) CY is approximately equal to MP.
That is because they are corresponding sides, they are the short side of each triangle. And since the triangles are equal, CY and MP are also equal:
[tex]CY\cong MP[/tex]c) for the same reasons as the previous two, PK anf AY, are corresponding sides:
[tex]PK\cong AY[/tex]d) and e)
The corresponding angles of Y and K are represented in the following image:
rrespon
A population grows according to an exponential growth model. The initial population is 224 and the population after one year is 263. Complete the formula where P is the population and n is the number of years.: P=224*(___)n
Round your answer to three decimal places.
The equation of the population function is is P = 224(1.17)ⁿ
How to complete the equation?From the question, the given parameters are:
Initial population = 224Population after one year = 263The above parameters imply that the rate of change of the population every year is
Rate = Population after one year/Initial population
Substitute the known values in the above equation
So, we have
Rate = 263/224
Evaluate the quotient
Rate = 1.17
The exponential function can be represented as
P = Initial population * (Rate)ⁿ
So, we have
P = 224(1.17)ⁿ
Hence, the complete equation is P = 224(1.17)ⁿ
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The required rate of the increase in the population is 17% and the equation is fulfilled as P = 224 (1.17)ⁿ.
As per the question, the population of the 2 years are given as 224 and the preceding year's population is 263 and equation is illustrated the exponential growth is given as P = 224(__)ⁿ. The blank space in the equation is to be filled.
The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
The given function of the population is incomplete as rate of growth is missing, So,
The rate is given as,
Rate = 263 - 224 / 224
Rate = 0.17 or 17%
Growth = 1 + 0.17 = 1.17
now, put this growth rate in the blank space.
So,
P = 224 (1.17)ⁿ
Thus, the required rate of the increase in the population is 17% and the equation is fulfilled as P = 224 (1.17)ⁿ.
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lana 15:02If two events A and B are independent and you know that P(A) = 0.3, what is the value of P(A|B)?
Since the events are independent, we have the following property:
[tex]P(A)=P(A|B)[/tex]That is, the probability of A is the same as the probability of A given B (since the events are independent, event B does not affect event A).
So, if P(A) = 0.3, therefore P(A|B) is also equal to 0.3.
To the nearest whole foot, how many feet would it be to walk diagonally across this field? A. 42B. 50C. 65D. None of the above
What are the explicit and recursive formulas for the sequence 540, 180, 60, 20, ...?
Here we have a geometric sequence, the recursive formula is:
Aₙ = (1/3)*Aₙ₋₁
And the explicit formula is:
Aₙ = (1/3)*ⁿ⁻¹*540
How to get the recursive formula?
Here we have the following sequence:
540, 180, 60, 20, ...
This seems to be a geometric sequence, to check this, we need to take the quotients between consecutive terms and see if we get the same thing.
180/540 = 1/3
60/180 = 1/3
20/60 = 1/3
So yes, this is a geometric sequence where the common ratio is 1/3, so each term is (1/3) times the previous one, so the recursive formula is:
Aₙ = (1/3)*Aₙ₋₁
And the explicit formula is:
Aₙ = (1/3)*ⁿ⁻¹*A₁
Where A₁ is the first term, in this case 540, so the formula becomes:
Aₙ = (1/3)*ⁿ⁻¹*540
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Figure L is the result of a transformation on Figure K. Which transformation would accomplish this? FigureL Figurek 5 4 2 2 -4
Answer is the first option, a reflection over the y-axis
Two Way Tables, URGENT
Step-by-step explanation:
a) modal number is 3
b) mean is x = ∑fx/n
= ((5•1)+ (2•10)+(3•15)+(7•4)+(3•5))/(5+10+15+7+3)
= 113/40
= (Decimal: 2.825)
The following triangles are not similar. Determine the ratio between AMCD and AOLN. Howcould you change the measurement(s) to make them similar?
The ratio between MD and DC IS
[tex]\frac{MD}{DC}=\frac{14}{6}=\frac{7}{3}[/tex]The ratio of ON to LN
[tex]\frac{ON}{LN}=\frac{49}{21}=\frac{7}{3}[/tex]The ratio CM to CD
[tex]\frac{CM}{CD}=\frac{12}{6}=\frac{2}{1}[/tex]The ratio of OL to LN
[tex]\frac{OL}{LN}=\frac{40}{21}[/tex]To make the
BK has endpoints B(1,4) and K(4, -3). Rotate BK clockwise 270 degrees about the ongin. Part A: Write an algebraic description of the transformation of BK. Part B: What are the endpoints of the new line segmente
B ( 1, 4)
K (4, -3)
We plot the points and after that, calculate their angles, then we measure 270 clockwise to calculate the new points.
The endpoints of the new segment are
B' = (-4.5, 1)
K' = (3, 4)
These are the points of the new segment
Please help I need to graph this and i can only have two points
Given the function:
[tex]f\mleft(x\mright)=\mleft(x+2\mright)\mleft(x-4\mright)[/tex]You can rewrite it as follows:
[tex]y=\mleft(x+2\mright)\mleft(x-4\mright)[/tex]You need to remember that the y-value is zero when the function intersects the x-axis. Then, you need to make it equal to zero, in order to find the x-intercepts:
[tex]\begin{gathered} 0=\mleft(x+2\mright)\mleft(x-4\mright) \\ (x+2)(x-4)=0 \end{gathered}[/tex]Solving for "x", you get these two values:
[tex]\begin{gathered} x+2=0\Rightarrow x_1=-2 \\ \\ x-4=0\Rightarrow x_2=4 \end{gathered}[/tex]In order to find the vertex, you can follow these steps:
1. Find the x-coordinate of the vertex with this formula:
[tex]x=-\frac{b}{2a}[/tex]To find the value of "a" and "b", you need to multiply the binomials of the equation using the FOIL Method. This states that:
[tex]\mleft(a+b\mright)\mleft(c+d\mright)=ac+ad+bc+bd[/tex]Then, in this case, you get:
[tex]\begin{gathered} y=(x)(x)-(x)(4)+(2)(x)-(2)(4) \\ y=x^2-4x+2x-8 \end{gathered}[/tex]Add the like terms:
[tex]y=x^2-2x-8[/tex]Notice that, in this case:
[tex]\begin{gathered} a=1 \\ b=-2 \end{gathered}[/tex]Then, you can substitute values into the formula and find the x-coordinate of the vertex of the parabola:
[tex]x=-\frac{(-2)}{2\cdot1}=-\frac{(-2)}{2}=1[/tex]2. Substitute that value of "x" into the function and then evaluate, in order to find the y-coordinate of the vertex:
[tex]\begin{gathered} y=x^2-2x-8 \\ y=(1)^2-2(1)-8 \\ y=1-2-8 \\ y=-9 \end{gathered}[/tex]Therefore, the vertex of the parabola is:
[tex](1,-9)[/tex]Knowing the x-intercepts and the vertex of the parabola, you can graph it.
Hence, the answer is:
←
In a test of a sex-selection technique, results consisted of 284 female babies and 15 male babies. Based on this result, what is the probability of a female being born to
a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
The probability that a female will be born using this technique is approximately
(Type an integer or decimal rounded to three decimal places as needed.)
Does the technique appear effective in improving the likelihood of having a female baby?
O No
O Yes
The probability of the girl being born to a couple is 0.949. Yes, it is effective in increasing the likelihood that the baby will be a girl as the number of girls is more than the number of boys.
What is probability?
Probability means possibility. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Given
In a test of sex-selection technique, results consisted of 284 female babies and 15 baby boys.
Total children = 284 + 15 = 299
The probability of the girl being born to a couple will be
[tex]P = \frac{284}{299}[/tex]
P = 0.9498
Thus, the probability of the girl being born to a couple is 0.9498.
Yes, it is effective in increasing the likelihood that the baby will be a girl as the number of girls is more than the number of boys.
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Evaluate.
34+(12+14)2⋅2
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
=1.875
Step-by-step explanation:
Add: 1/
2
+ 1/
4
= 1 · 2/
2 · 2
+ 1/
4
= 2/
4
+ 1/
4
= 2 + 1/
4
= 3/
4
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 4) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 4 = 8. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one half plus one quarter is three quarters.
Exponentiation: No. 1 ^ 2 = 3/
4
^ 2 = 32/
42
= 9/
16
In other words - three quarters raised to the power of squared is nine sixteenths.
Multiple: No. 2 * 2 = 9/
16
* 2 = 9 · 2/
16 · 1
= 18/
16
= 9 · 2/
8 · 2
= 9/
8
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(18, 16) = 2. In the following intermediate step, cancel by a common factor of 2 gives 9/
8
.
In other words - nine sixteenths multiplied by two is nine eighths.
Add: 3/
4
+ the result of step No. 3 = 3/
4
+ 9/
8
= 3 · 2/
4 · 2
+ 9/
8
= 6/
8
+ 9/
8
= 6 + 9/
8
= 15/
8
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators
2(3 + v) =
Please help solve this problem and thank you
Answer:
6 +2v
Step-by-step explanation:
This is distributive property. That means you will multiply each term inside the parentheses by the term on the outside of the parentheses.
2(3 + v)
2(3) + 2(v)
6 +2v
Use the strategy to simplify 4/576Write the prime factorization of the radicand.442834O42/2832O 4./283²O4. 2882
To simplify the fraction we will need to facto
A soup can has a radius of 4.3 cm and a height of 11.6 cm. What is the volume of the soup can to the nearest tenth of a cubic centimeter?A. 1816.8B. 49.9C. 168.4D. 673.8
hello
to solve this problem, we need to identify the shape of the soup can first since soup is a liquid and carries the shape of whatever container its in.
volume of a cylinder is given as
[tex]\begin{gathered} V=\pi r^2h \\ \pi=3.142 \\ r=\text{radius} \\ h=\text{height} \end{gathered}[/tex][tex]\begin{gathered} v=\text{ ?} \\ r=4.3\operatorname{cm} \\ h=11.6\operatorname{cm} \\ \pi=3.142 \\ v=\pi r^2h \\ v=3.142\times4.3^2\times11.6 \\ v=673.9\operatorname{cm}^3 \end{gathered}[/tex]from the calculations above, the volume of the soup is equal to 673.9cm^3 which corresponds with option D
I need help answering this question The other values of x are 8 and 13
Given the modulus function expressed as:
[tex]y=|x-8|[/tex]Since the function is a modulus function, the dependent variables "y" will all be a positive value
Using the values of x to be -5, 8, and 13 to determine the ordered pairs
When x = -5
y = |-5 - 8|
y = |-13|
y = 13
The first ordered pair will be (-5, 13)
If x = 8
y = |8 - 8|
y = |0|
y = 0
The second ordered pair will be (8, 0)
If x = 13
y = |13 - 8|
y = |5|
y = 5
The third ordered pair will be at (13, 5)
The graph of the function is as shown below:
The Brock family uses up a
1
2
-gallon jug of milk every 3 days. At what rate do they drink milk?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
The rate at which the Brock family drinks milk is 4 gallon per day.
According to the question,
We have the following information:
The Brock family uses 12 gallon jug of milk every 3 days.
Now, in order to find the rate at which they drink milk, we will have to divide the amount of milk by the total number of days.
So, we have the following expression:
Rate at which they drink milk = 12/3 galloon per day
Rate at which they drink milk = 4 galloon per day
Now, this the simplified answer because this is a whole number and we can not solve it further.
Hence, the rate at which they drink milk is 4 galloon per day.
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15.) In the accompanying diagram, ABC is a straight line and BE bisects 4DBC. If m4ABD = 2x and m4DBE = 2x + 15, find m&ABD.
Using bisection, the measure of angle ABD is of m<ABD = 50º.
What is the bisection of an angle?The bisection of an angle is when the angle is divided into two angles of equal measure.
In the context of this problem, we have that the angle BE bisects the angle DBC, hence the measures of these angles are given as follows:
mDBE = mEBC = 2x + 15.
As shown in the diagram, the entire line forms a ray, meaning that the sum of the measures of the angles is of 180º, hence we can solve for x as follows:
2x + 2(2x + 15) = 180º
2x + 4x + 30 = 180º
6x = 150º
x = 150º/6
x = 25º.
Then the measure of angle ABD is found as follows:
m<ABD = 2x = 2(25) = 50º.
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Determine the reasonableness of a solution to a logarithmic equation
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equation
[tex]\log_3x=7[/tex]STEP 2: State the law of logarithm
[tex]\begin{gathered} If\text{ }\log_ab=c \\ \Rightarrow b=a^c \\ By\text{ substitution,} \\ \therefore\log_aa^c=c \end{gathered}[/tex]STEP 3: Substitute the given values in the question to get the correct answer
[tex]\begin{gathered} \log_3x=7 \\ x=3^7 \\ By\text{ substitution,} \\ \log_3(3^7)=7 \end{gathered}[/tex]Hence, Answer is:
[tex]\log_3(3^7)=7[/tex]OPTION A
drag the tiles to the correct boxes to complete the pairs not others will be used
The general form of the equation of a line is:
y=mx+b
Where m is the slope of the line and b is the intercept with the y axis.
Since the intercept is the point where the line intersects the y-axis, if a line goes through the origin, then is intercept equals 0, b = 0, which is the case for the first and last line, then, their equation looks like this:
y=mx
When the slope (m) is a positive number, the line goes up as x increases, when the slope (m) is negative, the line goes down as x increases, then the equation of the first line must be: y=x and y= -x for the last line.
For the second line, we can see that it crosses he axis at y= -3, then its intercept equals -3, that's why the equation of this line is y = x - 3
ill send a pic of the question :) plsss help me
We have the next information
4 cups of water
1 cup lemon concentrate
in total, we have 5 cups of lemonade
5 ----- 100%
1 ------ x
x is the percentage of lemon concentrate
[tex]x=\frac{100}{5}=20[/tex]the percentage of lemon concentrate in the lemonade is 20%
PLS HELP!!! Ill give 20 points!!!
Answer:
Step-by-step explanation:
22.57 cm inches are the net weight of the slope